More can be said here of course, but this old response from /u/totheblack may be of interest for you.

I'd like to explain why this question is difficult for me.

Dealing with D-Day specifically. To state that the 101st and 82nd were more competent than the German 91st Division, 709th Division and the 6th Parachute Regiment is such a hard call.

So much of what happened was influenced by strategy and operations rather than battlefield tactics.

For example, on the German side, we have the debate between Erwin Rommel and Gerd von Rundstedt (with Hitler being an ineffective ref) on the correct use of armor along the Atlantic wall, a debate that had enormous implications on that tactical level but had NOTHING to do with German tactical competence on the divisional level.

The choice to give anti-air sickness pills to the 101st and 82nd was MASSIVELY incompetent, but clearly involved some staff officers (I've never seen anyone be labelled as accountable for this mistake) and has nothing to do with how tactically competent the 101st was.

There are literally dozens of examples like this, that I don't wish to bore people with, which had implications.

So if we want to gauge battlefield performance we can say that the 101st succeeded in its job on D-Day and preformed admirably during the (bloodier than anticipated) Battle of Normandy.

Where does competence come from? Good training? Equipment? Leadership? Staff work? Achievable missions? etc etc etc.

I would argue that in Normandy on DDAY 101st (6,600 landed on June 6th with 1,260 casualties on DDAY) and 82nd were given an achievable mission while the 91st / 709th Divisions and the 6th Parachute Regiment were not.

In terms of your question, far more competent, I would argue no, not far more, but it depends on which specific event you are talking about.