World at War is an unofficial variant of Milton Bradley's popular game "Axis and Allies". It offers players the chance to play the game from the war's beginning, when France and Poland are not yet conquered.
World at War comes with new units such as destroyers and additional pieces for each country. Besides destroyers there are also cruisers, paratroopers and special troops for the major powers, such as SS Panzers, Russian Guards, U.S. Marines.
World at War allows any player to place newly purchased infantry in any territory they control regardless of whether there is an industrial complex there.
In World at War, Russia starts off with more income than Japan and Germany. Although, the Axis can conquer territories and make up this gap, the gap is pretty big. The 3 Allies have a huge economic disparity with the Axis. Probably realizing this, both the USSR and US start at Peacetime Production and basically may not use their military until under attack, which severely restricts their possibilities until the Axis Powers do attack. This is a higly realistic representation in game terms of the strategic and tactical choices the Axis had at the beginning of WW II.
Also, the Axis has some special abilities in this game. For example, Germany and Japan can each make a sneak attack. It's not quite the same as having 2 turns in a row but its similar.
In conclusion, WaW is a perfect variant for Axis & Allies - whatever edition you use.