When you are low budged you have no choice, you either have to be creative or go for a niche (or preferably both :D). With high budget you have more options.
The difference is more of "degree of creativity". With high budget you have to stop at some point and restrict your insane/sick parts of creativity but with low budget you can go for "invasion of pink bunny-patatoes on the planet of zombie-wolf-cangoorus" (I'm quite sure it's utterly creative and never done before in that combination). But also don't mix the definitions and don't mistake "creative" for "good" which are quite different things as I hope proved in the previous sentence :D