I actually think D Day is the best small theater game they made. Three things I love about this game. 1) You can finish a game in less than 90 minutes then change sides and play again. 2) The rule card system makes it so easy to learn and play. 3) Either side can win and it is not unusual for it to come down to the last Turn (basically Turn 9) where the Allies are trying to get that 3rd city and close out the Germans while the Germans try to save just one last unit in that same 3rd city.
Except for the old Pacific game I can not think of another Axis and Allies game that frequently comes down to the end with either side being able to win. Usually in other games they are contentious for a period of time than one side gains an advantage, and builds on that advantage, until the other side simply has no chance and surrenders. While not an Axis and Allies game, Fortress America (1986), made by Milton Bradley as one of the Gamemaster series as Axis and Allies was (1984), also has that great feel of tension and stress coming down to the last Turn to see who wins or losses.
As for game play the Allied air force is a huge tour de force if used properly. In the early and mid game Bombers should knock out undefended tanks and even go for lone artillery. Late game use them to whittle down the side of the board where the Allies need the most help. In the early and mid game Fighters should be used to interdict reinforcement areas. A German renforcement should never be able to move without getting shot at unless the Axis deploys major AA cover fire. Late game fighters should stack the lasts surviving city to keep the Germans from reinforcing it. It is very painful to have four fighters shoot at every reinforcement you are trying to bring into a city.
The strategic logistic difficulties are what makes the game fun. The Allies have to balance their attack on all three cities. Send too much into one area and then one bad die roll will finish you off quickly. The Germans have to fight efficiently and preserve their units; especially tanks to hold that one last city. DO NOT try and fight for the beaches, Force the the Allies to come inland then outmaneuver them and hit them where they are weakest.
I love this game.