pretty much the same meaning I'd rather see a movie / I prefer to see a movie. The only small difference is that "would rather" denotes a choice and "prefer" is more of an option.

Hola Pedro! I think the main difference is that if the object is a thing, you are more likely to use 'prefer': 'I prefer the red shoes over the blue ones.' But if the object is an activity, you are more likely to use 'I'd rather': 'I'd rather stay at home tonight. You guys go ahead and go out.' Note that you could also say "I prefer baseball over basketball", and "I'd rather wear long-sleeved shirts than short-sleeved ones". In the former sentence, the object is a thing (a game) and in the latter, the object is an activity (wearing a thing). I had to think a lot about this. I'd welcome comments from other native speakers. Ted