This may seem obvious, but apparently Axis and Allies 1941 has eliminated the construction of factories, and AA guns?
How do these changes affect the play of the game as compared to say, the Classic Edition?
AA guns tend to reduce the value of "strategic" bombing. Hence you would do this more (and spend more researching heavy bombers) than in other versions of the game.
There are many players that believe that heavy bombers unbalance the game, and one should not be allowed to research them. If they are disallowed, AA guns would be less necessary, and can be eliminated from the game to simplify it.
The construction of factories is most important for Japan and Britain, who start with only one (everyone else starts with two). Hence, it makes these two countries harder to play.
There are some problems with the Factory Rule. The first is that one costs a "flat" 15 IPCs to build. But that doesn't reflect the fact that factories are easier to build in some places than others (e.g. in "real life," it's almost impossible to build factory in Sinkiang). Second, most countries would not "export" aerospace technology, meaning that realistically, it would be possible only to produce infantry, but not airplanes in a foreign factory.
My impression is that the lack of factory construction and AA guns is a astrisk on the real change of the game, that there are half as many units and a third as much income. This reduction in units and money makes the game far more luck based than previous editions. You both have fewer die rolls leading to more deviation from your expected value, and you have very limited ability to replace loses. The game can easily be decided on the first round due to very good or bad rolling.
I am not saying that the game is not fun, we love it! But the out-sized effect of the die roll overshadows the lack of factory and AA (which you'll never have the spare cash to build anyway).