Well, I wouldn't say "A big thanks to you!" myself, it sounds rather unconventional to my ears. "A big thanks" is more often used in speeches and announcements: "I'd like to give a big thanks to X for all his hard work [etc.]" This is when talking to a group of people about someone, rather than to the person directly, although that person may well be present.
If talking directly to the person alone, I would say "many thanks", or "thanks very much", etc.