Never really tried this with an Allied win, although in one game, we did have the US/UK go after the Soviet Union. So it basically came down to US, UK, France and ANZAC against the USSR and China. The Western Allies won. USSR was pretty tough right at first, but eventually the US/UK overwhelmed them. China actually stuck out pretty good for a while because they built up a lot of men while Japan was getting whomped, but after the Soviets fell, it was just a matter of grinding down the infantry stacks until China was no more.
Now, we did try out world domination with an Axis win. First we made sure every Allied territory was taken and every Allied unit was eliminated. Then each Axis got 1 turn to build up and move some units around. Then it was ATTACK! Italy did do good as they had Africa, most of the Middle East plus Brazil, West Indies and Panama. However, Germany had all of France and with all those ICs and the Majors in W Germany and Berlin, they were able to build up a really large force and took out North Italy right away. There was just no way Rome could defend against the German Blitzkrieg.
Germany was in pretty good shape since they had E and Central US, most of Canada, the UK, All of Europe except for Italy and Greece and all of Western Russia up to Moscow, Stalingrad and the Caucasus.
As for Japan, they ruled the Pacific, Australia, China, India, most of Eastern Russia plus W US, Mexico and part of Canada.
While Germany was making more money, they ended up doing the bulk of the fighting with Italy which meant Japan was free to only have to deal with attacking Germany. With Italy rushing back to try and liberate Rome, Japan also landed troops in Southern Africa and took over a lot of territories from the Italians with little or no fighting.
Eventually, poor Italy was wiped out. Japan and Germany traded Central US several times. Japan managed to capture the Middle East, Caucasus and Stalingrad, but never managed to take Moscow from the Germans. It took several rounds (this was a LOOOONG game) but the Germans started pushing the Japanese back in Russia and North America. After recapturing Stalingrad and the Central US, then manageing to take Western US, Germany just kept pushing and it got gradually worse for Japan. Germany finally won it all, and I think it took about 20 rounds beyond what it took to defeat the Allies.