Well I think I can simplify this
Punisher = 30 years of established feats
Big Boss = 3 games worth of feats
Punisher = Has lost but has also faired well against characters like Daredevil, Moon Knight, Bullseye and Spiderman
Big Boss = has gotten beaten on by a guy who couldn't damage concrete with his bare fist, has gotten one shotted by an overweight black man.
If you threw Punisher in MGS during the Cold War Era he'd end up steamrolling anyone there. The most dangerous opponents that Big Boss fought were Null and Gene, Null being barely a teenager, can deflect bullets but little to no skill and psychotic episodes. Gene has superhuman speed but Zero Shift wears him down fast which allowed BB to beat him.
If you put Big Boss in Marvel he'd GET STEAMROLLED by the characters that Punisher fights. Big Boss would not survive more than a few seconds against Daredevil, Moon Knight, Bullseye or Spiderman. Daredevil has batted bullets back which is far more impressive than Null, and unlike Null is actually skilled. Bullseye's accuracy feats make Ocelot look like a child with down syndrome holding a gun.
A rookie Ocelot would of killed Big Boss if he wasn't an idiot and had his gun jammed.
Big Boss and his enemies don't compare to Punisher and his enemies. Big Boss has no peak human stats, in any fight between Frank and BB, Frank would kill him quite easily unless the scenario is heavily in BB's favor.