Assuming that I have sufficient balance in multiple programs that see the same partner award inventory, however, there are reasons to choose one over others.

Say there is plenty of LX F inventory available on the SFO-ZRH flight (yeah, yeah, I know...) and I want to book the trip. Using US miles would limit my flexibility vis-a-vis stopovers and creative routings versus OnePass for additional stops/destinations as part of the trip.

Or if I want to fly from NYC to LON on VS in Upper Class and there are seats available I'd much prefer to redeem points from ANA for the trip than from VS's own program based on the total costs involved. Now that ANA charges YQ on those awards it is a bit tighter between CO and NH for that same award but it is certainly worth considering both options.

Of course, if I have an infinite balance in all the programs then I don't care nearly as much about the details because I can just redeem whatever I want.

Every program has its pros and cons and there are some great quirks in the various programs that get you more value than comparable earn/spend on other programs. I think that the question is too broad to give a simple answer to but it is certainly more nuanced than the "whomever has inventory" answer would suggest.