It will be difficult to measure, especially when you add in more than two players. Just examining two players for a moment here. It is usually more advantageous to go first during the first turn, because you get first race selection. After choosing your race, the new selection is revealed. If your opponent was only allowed a single turn, you could calculate the best move for every race before the revealed race, and determine the best move possible (after the new race is revealed, you can add it's best move into your calculations). If you only played one round, you will get the first attempt to take empty territory, and your opponent might have to attack you to take territory.
The exception to the above would be when a powerful race is revealed. This is less likely to happen when compared to the 6 starting revealed races.
An examination of the last turn is similar. The player who is going first has the opportunity to take any unclaimed regions (if any) before his opponent.
For the most part, this is a game of open information. Going first is an advantage in 2-player, because you could calculate your optimum move and your opponents optimum move that turn. In subsequent turns, you will get the first opportunity to go into decline. The only random events (race selection) favor the first player. In multiplayer though, who each person decides to attack has probably a greater effect on winning. If every player played optimally, I think the first player would still have the advantage most of the time, but that is a much more difficult question to solve.