They both just mean "really big". However, "massive" is a little more formal than "huge" so I suppose if you wanted to be a little more dramatic and emphasize the awe-inspiring nature of something's size, you could say "massive". "Huge" on the other hand is less formal and thus used with things that might not be genuinely large. For example, you're more likely to hear "a huge milkshake", rather than "a massive milkshake". But essentially they're the same and can be used interchangeably.