They are very similar. "Would like swimming" is a little more vague and slightly less certain, and would more likely be used when talking about someone else. Also, "would like swimming" requires a specific object - like "here," "in that pool," etc. For example, if I could say, "Suzy would like swimming here," and it sounds like I know what Suzy likes, and that she would probably like swimming in this particular place. On the other hand, if I said "Suzy would like to swim here," it conveys the idea Suzy definitely wants swim, that she has expressed that desire. Hope that makes sense.