Hm, I think it's a completely different kettle of fish here. By Elder Scrolls protagonist I am assuming you mean Skyrim, since the other protagonists all have different established personalities. The Fallout protagonists are badass and go through a lot of things, but TES characters often end up rewriting reality in one way or another, I think. I might really be oversimplifying things here though, but let me try to give some examples!
The Agent through his meddling with a giant dwarven entity (my personal theory is that Sheogorath is involved due to some parallel thoughts) manages to break reality enough to cause a bunch of events to all happen at the same time. Multiple empires arise, multiple deities ascend. Odd business, but time gets broken.
The Nerevarine from Morrowind is the reincarnation of an ancient warrior who ends up rewriting reality to destroy a god using dwarven sound magic. He then proceeds to wipe the canonical floor with several other deities.
The Hero of Kvatch becomes Sheogorath, and Daedric Princes are powerful beyond imagination, especially one as dangerous as Sheo.
The Last Dragonborn has access to Thuum, which once again is altering reality through sound. He also manages to banish Alduin, who is (or will become, depending on deep TES lore theories) one of the aspects of the chief deities and who is heralded to end the world as it is known.
In my opinion I think the TES characters would almost always prevail. Guns might be guns, but magic is magic after all, and the magic in TES often seems to go beyond what I believe badassery could handle.
OFF is a nice game for cute children.