Not your screen monkey (he/him)
He is better, his attacks do far more lethal damage for instance (1 hit on low level guy is a kill, low level guy can hack on you all day and do squat). Remember 'hits' are rather abstract in many respects.
But I don't think you want them operating on the same threshold. A higher level character may do more damage with a hit but without increases in his ability to hit, he bears the same chance of doing none. If you try to work the the narrative, he may be better at exploiting an opening in his target's defense because he's more likely to take the fight out of it, but he's no better at making an opening. And, again, he's no better at hitting a target on the archery range than a neophyte. Those ideas seem wrong to me.