I don't know all of the ins and outs of the literature, but the basic problems here go back at least to Bentham and Mill, who had a dispute about kinds of pleasure and pain. Bentham took the view that all pains and pleasures were on the same footing. A human appreciating a work of art is no different from a pig appreciating a good roll in the mud. Mill took the view that pains and pleasures had more internal structure. Of course, for both Bentham and Mill, pain played a big part in the moral calculus. General concern about the moral standing of animals goes back a lot further: Descartes, for example, claimed that we have a moral certainty that animals have no souls -- otherwise, we couldn't eat them -- but it's not clear to me whether he connected this to pain.

More recently, the debate seems to be about the degree to which an analogical argument works that takes us from human pain to animal pain. See, for examples, an older article by Singer (excerpts only) and a newer article by Allen et al (pdf). But for most of these people, the issues are not theological.