Switch and change are both OK but it should be "seats"

They are both ok but I’d use “change” if I’m asking a stranger to give me his airplane seat, for example. But if I’m at the movies with my children and one can’t see the screen because there is someone tall in front of her, I’d say “Here, let’s switch seats”. Switching is fast and easy. It would be a little presumptuous to use that with a stranger, since it minimizes the request. “I have a favor to ask, Sir. Would you mind if we changed seats so that I can sit next to my wife?” “You don’t mind switching seats do you?” (Implies that it would be unreasonable to say no)

In this context both verbs are equally suitable. As Simon says, it should be seats.

My first thought was that there was no difference, but I think DavidK makes a good point -- the word "switch" does imply that it will be fast and easy. "Change" is probably better for making a polite request. The difference is very slight, though, and not too important.

Technically to change seats would be to actually change the physical seats over or replace the seats. But we do use and say either change or switch, because switch implies also an element of changing, but not as its main first primary definition from dictionaries. Change in any dictionary equals to alter "change" for an exam it would be best to use switch. I think: but be guided by others.