Mid game is more important, as it sets the framework for how the rest of the game will progress. You can make a comback by mid-game, but after that, it becomes very hard to win if you aren't already.
Essentially, Midgame>Early Game>Lategame.
Midgame is most important for two reasons. First, because it's when most Demigods start to really play to their strengths, but also because each side will begin gaining access to important upgrades(cats, and later giants). For this reason it's imperetive that you keep the pressure up during this time. Likewise, it's at this point where you can turn the game around if you've been keeping your warscore up. At this point in the game, DGs will be gaining enough power to push, and generals will gain much of their killing power, moving the game forward at a much faster pace.
I like to end the game around the midgame period, as Erebus' skills tend to scale fairly badly after the midgame point(although his stats scale very well after that point).
