I've made fireplaces out of 5mm plate with the TIG. Mine goes up to 160A. I did two passes and used a 3/32 rod.
MIG is for when you're in a hurry or don't have three hands. I would always rather TIG because I'm doing it for fun and all practice with the TIG will help on the next bike frame. I probably would get a MIG if I did a lot of car body stuff though just because it's going to be difficult to reach.
TIG brazing is also a blast and I use it for braze-ons, bridges and sometimes dropouts and fork ends. I read recently that WRC roll cages are TIG brazed throughout so it ought to be fine to actually make a whole frame that way.