Which Okay so: If you're paying attention you should know by now that the particle は is the topic marker. It marks the topic of the sentence. Basically meaning that everything after the は is the topic and everything after it is a question or a statement about the topic.
With that knowledge:
The first sentence is: 猫はどっちですか the topic of the sentence is 猫, and what are we saying about that topic? we're saying 「どっちですか」which means "which one out of the two is it?". So this would be used maybe when you're walking to your friends home and on the way there you two are talking and he tells you that there are two cats in his house, but only one is his own cat, the other could be his mother's or something, and then he tells you more about that cat that he owns. You then arrive at his house and see two cats, so you could use 「猫はどっちですか？」 to vaguely ask which one is his, which one is the cat you were talking about.
The second sentence, どっちは猫ですか Well here, first of all, you can't use は like that, directly after a question word (question words are words like どこ、どれ、だれ、どっち、どちら、どの), you have to use が instead of は, so the correct way to ask this is どっちが猫ですか Now this just means "out of the two, which one is a cat?", like maybe you have a crocodile and a dog in front of you, and you don't know any animals because you've just woken up from a 30 year long coma and have forgotten everything except Japanese and the word for a cat for some reason, so you think "hey maybe one of these is a cat" and then you ask 「どっちが猫ですか」to find out which one of them is a cat
tl;dr: first one means "Which one is the cat?" while the second one means "Which one is a cat?"
So to ask which one is a cat you should use the second sentence, except with a ga there, instead of ha.