There are many advantages to going first.
Your 3rd turn is safe from attacks. For instance in a game where people will discard down to 3 "every" turn, you will get 3 turns of playing with 5 cards, while everyone else will get 2. This advantage can be very significant as dominion lead can snowball.
You will have the most chances to give away curses.
You have first dibs at all piles. If any pile of good cards runs out you have a chance to have the most.
You can take a province and end the game denying everyone more turns. So in a game where everyone is tied after an equal number of turns with 1 province left, you can take a province and win.
The tiebreaker in no way offsets this.
I would recommend letting everyone take the same number of turns, and letting players buy virtual cards from depleted piles on the last round. Even with this and the tie breaker i do not feel like it funny offsets the first turn advantage.
The only thing that may help more than going first is 3/4 vs 5/2 but that is fixed pretty easily