It would be really weird if philosophy didn't acknowledged any differences between humans and animals, since the humans are those doing philosophy, not the animals. One difference is how animals might be in doubt between two decisions like humans, but they won't get into the cartesian state of recursive doubt until they question the existence of an outside reality itself that makes them unable to act. If that state was a real experience from Descartes or just an hypothesis he poses as real is another question entirely.
The real issue with your question is that you can't talk about fundamental differences at the level of biology, only about differences in reaction to your biological experiments. There might be fundamental differences that aren't easily reproducible and might not be object of scientific experimentation, but they are perceived by men over time and have a symbolic relevance, leading to myth. Religious doctrine like those you mention are set in consequence of myth, and if you are really interested in knowing the fundamental differences, setting those aside is like a police investigator throwing away evidence that doesn't seem to be useful at the time.
Considering this, asking if there are any philosophical ideas about the difference between human and animals specifying the perspective of our behavior, intelligence, abilities and role in the universe taking religious concepts aside is absurd, since having those concepts is a major difference, and if not the most important and most studied in philosophy, one of the most. The religious ideas don't come out of nowhere, and as far as I know, animals don't do that.
Even if you try to set those concepts aside, they will come back in one way or the other, but you won't notice or you will be in denial if you assume they aren't relevant. For instance, you may set religious concepts aside and follow Singer's Animal Liberation suggested by another answer, which ultimately leads to the conclusion there's no fundamental differences between humans and animals. If that's the case and animals feel pain, then it's morally wrong for humans to explore them. However when we explore plants and destroy wildlife in order to plant crops, we are also putting ourselves ahead of the animals which lived there. We also don't know if the plants themselves don't feel pain and don't suffer, and the same reasoning applies. The obvious conclusion is that in order for men to survive, it has to cause suffering to someone or something, and its existence is inherently wrong in some way. You'll find that as a symbol in most cultures, and the myth from it leads to doctrine in many religions. Many cultures have an origin myth where men lived in a state of non-suffering, and then did something that lead him to a suffering existence. Christian doctrine calls it the fall of man.
If you set the religious concepts aside as if they weren't part of men's reality while doing a philosophical investigation, they will come back and bite you from some other side. It's inevitable. Notice that this has nothing to do with your personal religious beliefs.
You have a few good philosophers who investigated what happens with mankind when the fundamental concept of human and animal existence are reduced to the same thing, which is the other side of the utilitarian ethics from Singer and others. This relativization of the human condition is what Eric Voegelin ultimately links to ancient gnosticism and their modern siblings, communism and nazism. Voegelin might be a hard read, but Hannah Arendt's The Origins of Totalitarianism is easier, although the relation to your questioning might not be so obvious.