Are there any reasons to pick one game or the other when I’m on the button, e.g. is button-position giving more of an advantage for one?
You might prefer to be dealer at NLH than at PLO on advanced tournaments when the blinds are high in relation to stack and there are no limpers, because it is more difficult to defend blinds at NLH than at PLO. At the dealer side, it is easier to stole blinds at NLH than PLO; when you try to stole blinds in NLH you have less chances to be called.
The reason is every Omaha hand has a chance ~35% in head-ups against a strong hand, wich is not the case for Texas Holdem hands. Also, as it is Pot Limit, you will never have a big increase to equalize, normally 3,5x blind is the maximum you will face. When more than one player atacks your blind in Omaha, your odds decrease, but it is still better than playing a residual Holdem hand.
Said that position is even more important at Omaha than at Holdem.
"10. Position, position, position
Yes – position. In Pot Limit Omaha, having position over your opponents is infinitely more important than in Texas Hold’em. Some hands that are quite playable in position become easy folds out of position – and vice versa. So, every time you’re considering playing a hand in PLO, first think about whether you’ll have position and, if not, what you could do to change it (by raising or three-betting, for example, to get players behind you to fold)."
Maybe that is not the case for advanced tournaments, but at least at cash games, definitely I would choise PLO being the dealer to make more profit of the fact you have position over all the other players.