Interesting scenario, although in WWII the armies had more advanced and deadly weapons (Tanks, artillery, infantry rifles and machine guns, e.t.c.) without airplanes it would be much more difficult to break a defensive line, no bombardment of cities and industry means no moral penalty for citizens, a false "eyphoria", an uninterrupted production and much more easy replace of casualties.
So i can say that this war would be last much longer maybe 10-15 years until one of the opponents exhausted it's resources.
The German Blitzkrig wouldn't work, the Battle of Britain would have been something compleatly different if it would happened at all. Plus D-Day would have a much larger death toll and might not have worked if paratroopers wern't sent in behind enemy lines to disrupt German communication and supply lines. Pearl Harbour wouldn't have happened the way it did. The US would of had a much harder time trying to defeat Japan in the Pacific...
The whole face of that war would have been different if plains didn't exsist.
-no pearl harbour
-no battle of britain
-blitzkrieg would have been vastly slowed down so france may not have been conquered as quickly = greater cost of german tanks,infantry etc and the same in russia
-british supply convoys in the med would have not suffered air attacks so the 8th army and malta would have been better equipped with supplies
-no bombing on german cities would release thousands of men and artillery for front line service
-no paratroopers to protect the flanks of the landing troops on d-day