Both are strong. I think a well played Thresh is probably the best support in game right now. But like everyone else has said, do you want to support or jungle?
Currently, Nautilus is my favorite champ in the game. I play jungle mostly, and he is my go to for sure. His pre 6 is shaky, but you have a shield that scales with bonus HP on top of a root, a hook, an AOE slow, and a targeted unavoidable knock up into a stun. HP and CDR are your biggest friends (Kindlegem <3) and if you get kinda fed, a Wits End on him is VERY satisfying and entertaining :) Always run MS Quints and Mobility Boots on him though, cuz the Big Daddy is hella slow.
To answer your question though, I'd say Thresh is the better choice overall.