They both sound natural! :) To me, "swimming" and "reading" sound like names of hobbies, while "to swim" and "to read" would refer more to the actions (like maybe you think the action of swimming is fun, but you don't swim regularly as a hobby) However, you can also say "I like to swim" when talking about your hobby and you can say "I like swimming" when you are talking about the act of swimming. In this case, overall, word choice is far less important than the context of conversation!

Both sentences are correct. They basically mean the same thing and you could use them interchangeablly. It is just a matter of which form of the verb you want to use - the infinitive form of the verb "to swim" or the gerund form of the verb, by adding "ing" to the verb and taking away the word "to".

Note that there are other meanings of "I like swimming" and "I like reading" though. Which is the better way to learn the material? Reading or listening? "I like reading." (Doesn't mean that I personally like to read, but that I think reading is the better method.) "Do you like watching the Olympics?" "I like swimming. My kids did that when they were young. But otherwise I don't pay much attention to the Olympics."