I wouldn't say he's leagues below Matt and Danny. They're definitely more skilled but I'd say he's a tier or two below them (they're a "9-10" level, while he's a strong 8). The Russos have confirmed that the reason for Cap's massive and continually increasing jump in skill since The Winter Soldier can be attributed to his enhanced memory which allows him to master skills far faster than any normal human.
If we're arguing technique, as a martial arts nerd, I'd argue that MCU Cap actually shows better and more crisp technique as well as complex maneuvers compared to Matt or Danny who have a tendency to brawl and get sloppy when they get desperate (plus the MCU movies have a bigger budget/better choreographers so naturally Cap comes off looking more skilled). I also think you're underselling Cap's skill considering his feats - he's used his skill to overcome or stalemate opponents who:
A) are massively superior in stats - eg. Iron Man, Spider-Man, Ultron Prime
B) are equal in stats and have equal or greater training - eg. Winter Soldier (who has literal decades of HYDRA training and experience) and Black Panther (who has trained his whole life) who he fought while also fighting off War Machine.
There are also a lot of caveats to the feats you mentioned for Matt. He may have taken a bullet to the head but it was because of his helmet AND because Frank wasn't aiming to kill him. And he still was out of commission. We also don't know the circumstances of how he survived the cavern collapse so it's hard to quantify that as a feat. And when it comes to environmental advantages, Cap uses his environment just as much, if not moreso than Matt does (look at his fights with Spider-Man, Ultron or Crossbones soldiers). I'd also argue that Cap is actually more agile and acrobatic than Matt (though that could be attributed to his physiology). He's pulled off feats of agility that Matt couldn't.
As much as I love Matt, I don't think he's got the feats to say he could significantly hurt Cap, let alone knock him out. Cap's taken a prolonged ground and bound from a bloodlusted Winter Soldier who has shown the ability to punch through solid steel and concrete. He's taken hits from Loki, Ultron Prime, Spider-Man and Iron Man without significant injury. He's fallen from heights upwards of 50 feet onto concrete without injury. He's taken direct hits from grenades, Chitauri blasters, repulsor beams and Ultron blasts - all without a scratch.
One on one, I just don't see Matt being able to do any significant damage to him.
You agree with this shit?