For the purpose of this discussion I assumed that had already happened (in life, let alone on gaming, I usually start by asking someone nicely to do something before deciding whether I need to insist, since that's basic politeness) and the player saw no reason to change.
I guess I should have mentioned that part, given that this thread has plenty of DM distrust in it.
So yes, assume the asking part has come and gone. Presumably everybody is just fine with player abilities being nerfed by the player themself.
Ok then then the next big question is why is that player doing a lot better than the other. For me that would be a key component in what I do next.
For instance: The player is simply more tactically astute in combat. In that case I would do stuff like add more creatures to encounters and tailor monsters to counter that player. Note: I would not do this for every encounter. There seems to be a belief around here, that every encounter has to be challenging or deadly.
There is nothing wrong with the player getting to strut their stuff occasionally.
Now, if the pc was simply better from items or feats, I would discuss nerfing the feat or item in question for something lesser and/or ban that from the game.
On the other hand, if the issue was a particular power or feature, then a discussion would be about what is the best approach to this. It would probably end in a nerf but it really depends on what the group thinks.
This gets back to the "Not trust the DM thing". One thing to remember is that most of us here are DMs and most are old. We have heard and often witnessed some of the horror stories and while there may have been uncommon they linger in the mind. Also in my experience, here on these boards, people have come in to discussions with an issue and talking about nerfing or banning this and that and have often never taken the obvious step of talking about it to the group.
Some times the fact that one player dominates in combat does not bother the other players and that is not their focus in the game. Some times it only bothers the player and the DM and sometimes it only bothers the DM. In the latter case the DM often feels they are not challenging the player enough only to find that in conversation that the players are fine with the way things are going.
One thing I will note, (and this references the fudging issue) is that so far in 5e I have not really felt the need to ban or nerf anything and no need to fudge.
I will note, however, that in my experience there is an increasing disparity between what the designers think is an ok encounter and what the party is capable of. Though that may very well vary a lot depending on group and playstyle.