The majority of games are decided by MM. Pre Brits as Axis you were pretty often on the stronger team just based off ladder rank because there was a much bigger selection of players, though imo Axis generally had an advantage in randoms due to both factions having late game units. When Brits arrived, the player base shifted massively in favour of Allies, giving them the advantage as well as finally having a decent lategame.
Since the player base has shifted back towards Axis favour slightly, once again they have the advantage due to MM, but I feel balance is pretty good right now in 4's unless you are too soviet heavy / have no Brits.
Does eventually turn into an arty fest if there is no clear winner, which ends up being pretty boring.
And what determine the amount of player Axis and Allied? The balance. Disproportion of Allied / Axis search game is a direct result of balance issue like ISG/Mortar dominance meta.