(he hates Devil May Cry so i dunno if hes lying or not)
That should have been your first clue, really.
Big Boss is an expert in CQC, knows how to handle multiple firearms and mix melee with a knife, stealth tactics, and by this time should be an expert in military tactic, but he's still a living, breathing human at the end of the day. But let's be honest here, Dante is a cocky mofo. He isn't going to take the fight seriously right off the bat. He's going to play around with Big Boss, makes some one liners, probably joke about his age, and shoot at him and swing his sword around before he DTs. Big Boss would need to have perfect timing and think five moves ahead of Dante just to keep up with his speed, but he isn't matching Dante in power. I could see him surviving the encounter, if only for taking advantage of Dante's cockiness, it's how Nero came out of his fight alive, after all.
Big Boss would need to learn what Dante is, study up on his bloddline, Devil Arms, and Batman plan that **** to best him. Unless it's DMC 2 Dante, then yeah, it'd be over in five seconds. That Dante doesn't mess around.