Well the AI doesn't like to purchase new aircraft... but the battle for air superiority was still a drawn out affair. I play on Manstein, so their starting FW190s and ME109s were... like 18 strength? Base 13+5 for Manstein. So for the first few turns, I was dodging the Luftwaffe as best I could, because they pretty much 1 or 2 shot even my best LA-5s. On such a large map though, this wasn't too hard to accomplish. So I bided my time and waited for more Soviet aircraft to arrive as reinforcement, and eventually I overwhelmed the Luftwaffe with sheer weight of numbers. Just in time too, I was getting a little irritated watching 18 strength Stukas completely obliterate my armored counter-attacks, heh.
As for the Tigers, yea pretty much had to ignore them and go after their supporting infantry and artillery and air defense units first. Each Tiger shots one of my units no problem, but each Tiger can only do it once per turn.

Without support units though, they floundered against combined infantry/57mm ATG(this thing is AMAZING), IL2, and strategic bomber assaults.
As you can plainly see though, it was an extraordinarily bloody affair, my infantry and tank losses are triple that of the Germans, not to mention all the other units classes I lost.