With top characters being more equal, attacking first becomes a disadvantage. The opponent knows what they have to do to win. Especially if they go with a defensive strategy of posting weak to middl...
Most of these matchups are based on efficiency when everyone has high level toons. So yes it matters, it makes a person have to decide whether they go in with undersized squads or not to squeeze out extra points. If youre attacking first you may not be going in with an undersized squad but the second team knows it has to take that risk.