Thanks, Pig with Pen!
Adventure! will give you much more powerful, world shaking characters. A millionaire telekinetic who runs a world spanning criminal empire would be an easy character to build in Adventure! In my opinion, and this comes from a year of playing Adventure! but not having run HEX, combat is going to be slower in Adventure! due in part to dice pool splitting and multi-step combat. So if you want much more powerful characters, slower (but still fun) combat, and an unusual sort of setting (the Trinityverse is neat, but it's definitely not right for a lot of folk) consider Adventure!.
Spirit of the Century (
my review) is going to give you more of a focus on the character and their past exploits through the Aspects system. The Tagging system is going to make Academics, Occultists, and other characters that exist largely to deliver knowledge from the GM to the Player a lot more fun to play. Mooks are easy to incorporate, and combat tends to notably favor the heroes (at least in my experience). If you want a pulp game set in the 1920s with a nifty twist (characters as defenders of the era) that sports really cool, but definitely non-standard mechanics, give SotC a try!
HEX is going to give you characters that are clearly exceptional, but who are much closer to being human than either of those games. HEX wants you to feel exceptional, but it places more emphasis on the human side of things. Weird powers are, well, weird and definitely worthy of exploration and awe. The setting is fantastic. Not only is 1936 a welcome change for pulp, but the Hollow Earth is very well done and offers an incredible number of options for adventure. The system is intuitive and should be easy to teach people, and with the Taking the Average convention a lot of unnecessary dice rolling is avoided. Unlike either Adventure! or SotC, HEX has a future product lineup that will expand upon the setting and character options to make it an even more robust world. If you want a smart, fun setting then you should definitely check out HeX.
So, there are some jumbled thoughts for you!