Epistemic Status: Provisional thoughts that seem likely to either a) be very worth sharing and expanding upon, b) invalid based on arguments I have not thought of, or c) replicating discussions that I'm unaware of.
I posit that moral suffering is maximal for agents of moderate sophistication, and that suffering of moderately intelligent non-human mammals and younger children are in some sense much more damaging and morally important than suffering of either less complex organisms, or older children, more sophisticated animals, and adults. If true, the implications go beyond the relative importance of humans and animals, and affects the moral relevance of the far future.
Humans at different ages
Most people seem to agree that physical pain isn't always suffering. For example, working out produces physical pain that many people describe as enjoyable because of the context that the exerciser puts around the activity.It is rational to undergo painful surgery to address a medical problem, and adults can reach a level of sophistication where they accept the painful process of surgery and recovery in order to gain something longer term. People who cultivate a mindset that contextualizes and abstracts away from their own suffering are even more "sophisticated" in a certain sense, and I would consider the pain from this surgery to be less morally objectionable than the same pain without the context. Infants never contextualize suffering. It seems plausible that they don't clearly distinguish between different levels of suffering either - for young enough infants, cold from a diaper change gets the same level of reaction as receiving a shot, or even undergoing a more major surgery. The length of time is arguably morally relevant, but they don't appreciate the difference between a minor short term pain or discomfort and a more major, longer term one.
Young children are able to contextualize their suffering, and by age one-and-a-half, my kids could understand that diaper changes are unpleasant for them, but they would (usually) volunteer to undergo them because they were aware that they would be happier with a new diaper. As children age, they become more able to appreciate this.On the other hand, in some sense the pain undergone by a five- or six- year old is worse than that undergone by an infant. They anticipate it, remember it, and are affected by it much more than a much younger child. Adults do the same - but there is a trade-off between the sophistication of context and the increased pain from imagination, memory, and cognitive appreciation of pain. I think it is clear from both my memory and my perception of my children that there are more intense feelings that occur in kids than adults.
Frans de Waal makes a clear case that humanity historically underestimates the suffering of animals. Catia Faria suggests that "all sentient individuals, including nonhuman animals, are morally considerable, irrespective of their species or other alleged species-specific attributes." Even simple animals almost certainly experience what we think of as pain. Lizards and birds suffer when injured. Insects seem to experience and avoid pain as well - though at some point it is less clear exactly how much of their experience is actually "experience" in a morally relevant sense.
It seems, however, that suffering as a morally relevant concept has some lower bound, and the focus on "sentience" becomes critical. Clearly non-conscious bacteria, reinforcement learning systems below a certain complexity, and similarly simple systems seem to have near-zero moral weight - because what they experience is not normally understood as suffering. As sophistication reduces past a certain point, the moral relevance of each animal falls. (I am not discussing the aggregate amount of total pain suffered, nor am I advocating anything like certainty about where this line lies. I'd suggest that moral responsibility seems to advocate for a precautionary principle in this regard.)
As we move towards more complex animals, we start to see more clearly relevant pain. More than that, the pain seems to have increasing moral weight. Temple Grandin and Catherine Johnson argue in "Animals in Translation" that (some) animals feel fear, and this seems to match our (potentially unreliable) intuition that higher mammals that can plan and reason about the future also can anticipate fear. In a very real sense, they suffer more than adult humans, because they have almost no control over their environment.
I would not advocate measurement of importance of suffering, but there are real implications to the potential for convexity. Most of these are unsurprising for effective altruists - animals are at least potentially more morally relevant than humans, and mitigating suffering means we should focus on reducing experienced suffering, rather than increasing life spans. As a perhaps more esoteric consequence, it argues that increasing intelligence may reduce morally relevant pain - and therefore parts of the far future where there has been an intelligence explosion are less morally relevant than the present.