Summary
There's a wide consensus that at least higher animals can consciously suffer. Even if we had doubts about this fact, it wouldn't much affect our expected-value calculations, because animals are so much more numerous than humans. It's sometimes claimed that humans suffer more intensely than animals because of deeper emotional experiences, but I think that raw pain itself represents a nontrivial fraction of the total badness of suffering, and even if we did count animals less, it again wouldn't much affect calculations (given their numbers).
Animal consciousness
Nearly all modern-day scientists agree that at least mammals and birds are almost certainly conscious of their emotions. The "Cambridge Declaration on Consciousness" was one clear expression of this consensus.
That animals can consciously suffer almost needs no discussion, but agnostics remain, some of them noble in spirit.
One agnostic animal advocate is Marian Stamp Dawkins, whose "Convincing the Unconvinced That Animal Welfare Matters" encouraged animal advocates not to claim that science knows that animals are conscious and instead to advance other reasons for caring about animals, including human-centered ones. In reply, Marc Bekoff wrote "Dawkins' Dangerous Idea: We Really Don't Know If Animals Are Conscious," arguing that Dawkins was ignoring too much of the overwhelming case for animal consciousness that already exists. There are many more debates of this type, but I'll focus on the Dawkins-Bekoff exchange here.
Scientific certainty vs. practical action
I think the most important distinction that needs to be made is between "certainty" in science and "certainty" in ethics. Dawkins is right that science should remain skeptical of animal consciousness and that we should seek out proof independent of existing assumptions.
But while Dawkins is correct that we don't know "for certain" whether animals are conscious, this statement is misleading to many laypeople who assume that she must mean the odds are around 50%. I don't know what she thinks the odds actually are, but I would give above an 80% chance of chicken consciousness and above, say, 85% for pig consciousness (compared against maybe 95% that you're conscious). With odds like that, it's best to say that the case is proved or else the public will misunderstand. Many people are not motivated by less than absolute certainty, and I think Bekoff is right that emphasizing scientific doubt is going to hurt animals on average. (Just look at what talking about uncertainty does for the global-warming debate.)
Evidence for animal consciousness
Now, Dawkins is totally correct that we don't understand exactly why animals are conscious. Indeed, we don't even know why people are conscious. What exactly does being conscious allow you to do that you can't do if you're not conscious? As blindsight demonstrates, you can walk and avoid objects without being conscious of them. If we ourselves didn't experience our consciousness through our own minds, then we would definitely have scientific doubts about whether people are conscious, too.
There are manifold articles demonstrating sophisticated, self-reflective behavior in animals that Bekoff and others take to imply consciousness, and indeed these are excellent pieces of evidence. However, they are not conclusive proof of consciousness because we can't even prove that humans are conscious using such tests at the present time. (In the future, once we really understand how consciousness works in the brain, we should be able to assess consciousness just by looking at the brain and what algorithms it's running.)
I think arguably the strongest reason we should believe animals are conscious is that they're close to us on the evolutionary tree, and their brain structures are remarkably similar. In "New evidence of animal consciousness" (2004), Donald R. Griffin and Gayle B. Speck note that "the search for neural correlates of consciousness has not found any consciousness-producing structure or process that is limited to human brains" (p. 1). And in "Building a neuroscience of pleasure and well-being" (2012), Kent C. Berridge and Morten L. Kringelbach comment:
Progress has been facilitated by the recognition that hedonic brain mechanisms are largely shared between humans and other mammals, allowing application of conclusions from animal studies to a better understanding of human pleasures. [...]
Some might be surprised by high similarity across species, or by substantial subcortical contributions, at least if one thinks of pleasure as uniquely human and as emerging only at the top of the brain. The neural similarity indicates an early phylogenetic appearance of neural circuits for pleasure and a conservation of those circuits, including deep brain circuits, in the elaboration of later species, including humans.
Probably dozens of other papers could be quoted in a similar fashion. Based on this, 50% is too low as a probability for mammal and bird consciousness.
Should we use other arguments to help animals?
What about the effort that Dawkins proposes: Making people care about animals for human-welfare reasons? If we could press a button to do this, I'd be in favor of it. But when we're parceling out our scarce resources for helping animals, I think this undertaking should go pretty low on the priority list. It's great if we can help animals in the short term in this way, but if we're going to prevent future humans from multiplying wild-animal suffering into the galaxy, we had better make sure our descendants actually care about animals. Even if helping animals sometimes coincides with human interests today, it's not guaranteed that will remain true in the future.
Finally, I did like this statement from Dawkins, as quoted in Bekoff's article: " ... it is much, much better for animals if we remain skeptical and agnostic [about consciousness] ... Militantly agnostic if necessary, because this keeps alive the possibility that a large number of species have some sort of conscious experiences ... For all we know, many animals, not just the clever ones and not just the overtly emotional ones, also have conscious experiences." (p. 177) It's totally appropriate to talk about probabilities and expected values in the right context, but my complaint to Dawkins is that among the general public, the language of uncertainty makes people confused and less motivated.
Is animal suffering less bad than human suffering?
Even if people agree that animals can suffer, they may suggest that animals suffer less intensely because they don't have the same high-level mental suffering that humans do.
In response, I would first point out that it's unclear whether the claim is true that animals have substantially less sophisticated mentation, at least "higher" animals like mammals. Animals show many of the psychopathologies that humans do and are used as models for depression when testing drugs. Elephants have death rituals. Crows appear to go sledding for fun. Marc Bekoff, Jonathan Balcombe, and other ethologists have written numerous books documenting the complex emotional lives of mammals, birds, fish, and even octopuses.
Secondly, what if we thought animals did suffer less? Well, I guess I would ask, How much less do they suffer? I don't think it's orders of magnitude less, and if not, then the basic calculations showing that, at the margin, animal welfare takes priority over human welfare would remain. Suppose you were a chicken being scalded and drowned alive in a boiling defeathering tank. How much less bad would this experience be if you didn't have broader thoughts about the end of your life, the injustice of your situation, how much you'll miss your friends, etc.? I suspect that the raw physical pain would overwhelm these subsidiary thoughts during the moment, and even if not, I don't think the higher-level thoughts would be vastly stronger than the raw pain.
Finally, there are many times when humans may in fact suffer less because of their understanding of the situation. Humans enduring a bout of food poisoning can know that the agony will end after a day or two and that their friends and family will help them in the mean time. Animals going through the same experience may have no idea what's happening to them, whether it will end, or what will become of their lives.
While it may be an illusion, I subjectively feel as though my daily experiences are less emotional, and hence less morally important from a hedonistic perspective, now that I'm an adult compared with when I was a child, because as a child I had less ability to regulate my emotional state.
Rolls (2008), p. 152:
In humans, grief may be particularly potent because it becomes represented in a system which can plan ahead, and understand the enduring implications of the loss. (Thinking about or verbally discussing emotional states may also in these circumstances help, because this can lead towards the identification of new or alternative reinforcers, and of the realization that, for example, negative consequences may not be as bad as feared.)
The points discussed above are fascinating to ponder, and it's valuable to hear from other people which of their own experiences they've found most unpleasant. That said, we modern humans live extremely comfortable lives compared with factory-farmed or wild animals, so it isn't surprising that most of our worst memories may be of purely emotional injury. In any event, regardless of where we settle on the question of the relative magnitudes of animal and human pain, physical and psychological pain, I don't think it's likely to tip the balance of our calculations about where our dollars and hours will do the most good.
Importance of self-awareness?
LeDoux and Brown (2017) consider a representation of self as crucial for emotion:
Without the self there is no fear or love or joy. If some event is not affecting you, then it is not producing an emotion. When your friend or child suffers you feel it because they are part of you. When the suffering of people you don’t know affects you emotionally, it is because you empathize with them (put yourself in their place, feel their pain): no you, no emotion. The self is, as noted above, the glue that ties such multidimensional integrated representations together (156).
This idea that selfhood is important for emotion strikes me as odd. My imagination of a strong emotion like pain is that it's mostly a message of "bad thing happening now!", and situating that pain within the context of me as someone experiencing it is merely icing on the cake. What matters most about pain is the strong motivation it produces, and that motivation doesn't seem to depend significantly on a concept of myself as the experiencer.
LeDoux and Brown add:
Tulving argued that autonoetic consciousness is an exclusive feature of the human brain (135). Other animals could, in principle, experience noetic states about being in danger. However, because such states lack the involvement of the self, as a result of the absence of autonoetic awareness, the states would not, in our view, be emotions.
Even if this hypothesis is true (for some sufficiently specific notion of "autonoetic consciousness"), it seems overly parochial to me to only count those kinds of minds as having emotions.