Being aggressive is the only way to play Mage Wars. If you never attack or damage your opponent in any way, you will lose every time. If you do damage your opponent, then you are by definition being aggressive :-P
It's possible in the future there might be alternate victory conditions, but until then aggression is the name of the game. The question is rather about your method of aggression. Does it start strong and wind down, or does it start with a whimper and build up? In both cases you want it to be fast enough to win within the time constraints. Wildhorn's comparison to a Formula 1 race is very apt.
Because of this sole focus on killing your opponent and being aggressive that is inherent to the game, Shad0w is correct that any tie breaking method needs to also focus on aggression or risk drastically changing that inherent nature. I do still like the "overtime" method, which only looks at the last few rounds of the game when control mages should be at their strongest and aggro mages should be at their weakest, but it is still a method that focuses on how aggressive the mages are being during that time. However, that method requires extra management and record keeping, with having to announce when overtime begins and then recording how much damage is dealt each round.
It's not overly complicated, but certainly is more so than the current method and I'm not convinced it would be any more fair. If I'm closer to killing my opponent than he is me, but he wins due to some lucky rolls in the last few rounds (even though I still end up ahead overall) then I may be a bit sore at my defeat. It may very well be that he would have won given infinite time because my lead was slipping, or perhaps I could have pulled off the win. Predicting the future is basically guess work and not exact, especially in a game this complex. It's still my favorite alternative, and I wouldn't be upset if some version of it was implemented, but after thinking about it I do think the current method is actually superior for being simpler and less biased.