I think they equivalent. Rat her DOES also mean prefer, but it also has the meaning of "some what" as in the example you use. Both are more common among the British, and Americans who wish they were Brits. The average American is more likely to say "pretty big." Quite, rather, and pretty are all "pretty/quite/rather" subjective and can be used interchangeably. Use your tone of voice or raise your eyesbrows to suggest the degree of bigness. :)

I think rather means prefer e.g .. i rather eat bananas to apples It means i prefer bananas than Apples. But *quite it means a quantity like. i am quite good at English It means that iam a little good at English and iam not very good at it P.s please if i made any mistake correct it i am an English learner thanks