The downside of comish veto is that you have to let trades go though that you're not wild about. In an advanced leagues (keeper, dynasty, salary leagues) this can lead to 3-4 world beater teams, 10 or so second division teams, and 2-3 absolute garbage teams that the poor comish tries to fill with new managers every year who are willing to spend 4 years cobbling the team back together.
That's worst case. And it only happens when some managers in your league consistently make bad moves, moves that hamper their team long term.
The downside of league veto is that it gets real petty, real fast. As soon as someone vetos because "you didn't get enough for Player X," that opens up the can of worms to basically veto any trade just because. Say you're working out a deal, and your trading partner takes your offer and goes to a third team, leveraging your offer into a better package from team C. Pissed off, you veto the trade. This happens all the time, and it leads to retribution, to more nastiness, and eventually to cliques, where some people trade with other people and categorically refuse to trade with others. THIS IS THE WORST.
The downside of league veto is FAR WORSE than the downside of comish veto. All you need to do is fill your league with managers that are at least in the ballpark of knowing what they're doing.