The common order in Russian is adjective precedes whatever it used for, so that's the reason you've figured out that "большое спасибо" is overwhelmingly more popular. Well, it's slightly more complicated than that, because Russian counterpart for English phrases in form "noun + is + adjective", like "the world is big" comes like "noun + adjective" like "мир большой", but this has nothing to do with you particular case, so let's just mention this fact but ignore it further.
So "большое спасибо" is indeed the most used form, however Russian is not that strict about order and in particular cases, in casual usage, the order can just be swapped, like in phrase:
Вчера в магазине видела такое платье красивое, но так и не решилась его купить.
Спасибо тебе большое, Пётр.
I'm not aware of any semantical differences or additional connotations that are exclusively specific for "спасибо большое". Both, for instance, can be say ironically or, say, passive-aggressively. Both can be a form of sincere gratitude.