In the west the allies mainly pushed them back by quickly wiping out the front line and forcing retreats, they didn't have many reserves. for battles that went several rounds germany won almost all of them. In this regard the allies plethora of artillery and planes, particularly typhoons was huge. On this note, I think that stukas and typhoons are easily the most important pieces to have, particularly with the limited front line where support units are so critical. Although the axis won I still feel that the allies have the advantage, by how much i'm not sure. They could have won the game several turns earlier if not for a failed attack on rome in which the allied front line was wiped out and the axis front line survived with a mere one troop, in general the entire allied italian campaign was mismanaged and, with the game, should have been over much sooner.
Yet again I had enormous difficulty doing anything with the Italians, I have yet to play a game where they do anything more advance a space into british territory before withdrawing hastily. the germans supported them with planes but a few lucky anti-aircraft rolls finished that. I think that for the italians to do anything german support has to be pretty substantial, both in planes and ground troops.
On the eastern front german had a pretty good time of things. I love how initiative works, even though poor rolls held the germans up at perekop for three turns. had it not been for that lack of luck I think that germany would have taken stalingrad and maikop for a couple turns and would have easily held budapest and bucharest.
In general I love the mechanics of the game. all the big changes including initiative, leaders, limited front lines, and air combat worked really well. One issue was sub attacks. Despite building a bunch of subs they never really got off the ground. hunter-killer attacks against them were wildly successful and few survived more than a turn or two, although perhaps this was due to britain's large shipbuilding program.
In general I think the allies have the advantage. In this game the allies played pretty risky tactically and few of their gambles paid off, particularly in italy. germany went heavy on the eastern front early and despite poor initiative and slightly substandard rolling were on the attack until mid 43ish.