Hey Amy! I hope you also appreciate input from non-native English speakers! But from my experience "a great deal" has a nuance of comparing it to others while "huge" is relatively independent from others. :) "A great deal of influence" = lots of influence while others might not have as much of it "Huge influence" = lots of influence while others might just have as much of it "Great influence" = a little less than huge But this is just my feeling of a language I wasn't raised with :-) Usually they might be used interchangably. Feel free to correct me, native speakers!