So thinking about the "why not both?" option, which I'm going to admit, I haven't seen many people who want the mundane Fighter offer that olive branch (so no disrespect, MockingBird), there is, sadly, a good reason why.
The improbability that a guy with "realistic" limitations (whatever those may be) can also coexist at the same power level as someone capable of superheroic feats. Sure, we all immediately think "well Batman" (or Hawkeye), but the thing is, those aren't "mundane Fighters".
Hawkeye's ability to never miss, even if it's some insane trick shot, or even shooting blind? Batman's 20 in all stats, mastery of all skills, and all tools, and a wide variety of Fighting styles?
Those are superhuman feats in of themselves. And we're not even talking about Batman vs. Superman here. We're not even talking about 80's action heroes- the "mundane Fighter" isn't John Rambo.
He (or she, or it) is Sgt. Rock. A competent and experienced soldier whose main schtick is they can take anything World War 2 can throw at them and not die.