Strictly MCU, Rogers has the best band to hand combat scenes besides Black Widow. He gave it to Batroc, put down an elevator full of trained agents, and completely outmatched Bucky.
That said, T'Challa had Bucky running everytime they saw each other. If we take in the account the facts of the movies, the fact that Rogers can fight AT ALL makes no sense. Like it was already said, T'Challa and Widow have been fighting since they were children and Thor, albeit a god, has over 1000 years of fighting experience. He damn near killed the frost giants entire race just for fun.
But Rogers raisin potato salad eating ass is the product of unfair writing. He should be in the same fighting class as Ant Man and Stark to be honest.