Most people do this intuitionally, and most people keep to make rationalisations of their intuitive judgements or construct neat logical moral theories in order to support them (and these theories usually fail to describe what they are intended to describe, because of their simplicity relative to the complexity of an average man's value system).
That said, for me an agent is the more morally significant the more is it similar to human, and I determine suffering by comparison with my own experiences and some necessary extrapolation. Not much useful answer perhaps, but I don't know of any better.
And you are hiding the complexity of "moral significance" in "similarity". Is a statue of a human more similar to a human than a horse? Is a human corpse? What if you take out the brain and replace it with a life-support system that keeps the rest of the body alive?
For a long time, I wanted to ask something. I was just thinking about it again when I saw that Alicorn has a post on a similar topic. So I decided to go ahead.
The question is: what is the difference between morally neutral stimulus responces and agony? What features must an animal, machine, program, alien, human fetus, molecule, or anime character have before you will say that if their utility meter is low, it needs to be raised. For example, if you wanted to know if lobsters suffer when they're cooked alive, what exactly are you asking?
On reflection, I'm actually asking two questions: what is a morally significant agent (MSA; is there an established term for this?) whose goals you would want to further; and having determined that, under what conditions would you consider it to be suffering, so that you would?
I think that an MSA would not be defined by one feature. So try to list several features, possibly assigning relative weights to each.
IIRC, I read a study that tried to determine if fish suffer by injecting them with toxins and observing whether their reactions are planned or entirely instinctive. (They found that there's a bit of planning among bony fish, but none among the cartilaginous.) I don't know why they had to actually hurt the fish, especially in a way that didn't leave much room for planning, if all they wanted to know was if the fish can plan. But that was their definition. You might also name introspection, remembering the pain after it's over...
This is the ultimate subjective question, so the only wrong answer is one that is never given. Speak, or be wrong. I will downvote any post you don't make.
BTW, I think the most important defining feature of an MSA is ability to kick people's asses. Very humanizing.