You can't compare people's emotions except by brain-scans. All emotions are self-reported other than that; so what you're really measuring is emotional expressiveness and subjective experience of emotions.
That said, from what I have seen, it seems like autistic people are, on average, about as emotionally expressive as neurotypicals. However, autistics have a wider range of expressiveness--there are more of us who are either very expressive or hardly expressive at all; as well as more of us who report feeling very intense emotions, and more who report feeling very little emotion.
The idea that autistic people don't have "hearts" is an incorrect stereotype. From all the things I've read, autistic people do not have an impairment in compassion. What we do tend to have, more often than NTs, are impairments in detecting emotion in other people. (There are hyper-empathic autistics out there, though.) So, we may have no clue that someone else is hurting; but once we figure it out, we will be just as compassionate as the average NT. Autism is not a problem of compassion; it is a problem of communication.
You are correct in saying that autistics are more often "self-centered" than neurotypicals are; but that's only a true statement when you use a specific definition of "self-centered". Consider a two-year-old (neurotypical) child, who has not yet learned to take another's perspective, whose theory of mind is still very primitive. He is quite capable of loving his mother and quite capable of caring about her when she is upset. However, he will not know how to take her perspective; so when she is upset, he may well try to comfort her by bringing her his favorite toy, because that toy would comfort him. He doesn't understand yet that his mother thinks differently. That is the "self-centered" action of a child (I have to put it in quotes, because it means a totally different thing from what it means in ordinary conversation). Many autistics are similarly unable to take another person's perspective. Most of the time, theory of mind does become available, though later than it does in neurotypical children, and usually through logical rather than empathic development. Rather than instinctively understanding how another person feels, many autistic people have to reason it out logically, which can take longer. So, "self-centered"... maybe, but not in the way most people define the term.