This is probably going to be a very difficult question to answer. Generally speaking, all else was never actually equal. Survival rates are dramatically effected by the strength of opposing forces and the tactics and logistics in various situations. I really can't think of any battle or campaign where all other factors were so similar that you could easily attribute differences in survival rates to uniforms. It is also important to note that the uniforms themselves would have different effects in different situations. The war had campaigns in deserts, on beaches, in open countryside, in forests, in all different seasons, etc. The effects of the uniforms on combat are going to vary dramatically across these settings, both in terms of the different camouflage effects and dealing with climate differences. I'm not sure you can really generalize about which uniforms were better when there were so many different conditions to account for.

The only example that I can think of where it made a real difference would be the first winter in operation Barbarossa. The German troops were properly equipped with cold climate gear but this has more to do with logistical and leadership issues than anything else. They had cold climate gear...it just wasn't issued. In other theaters like Africa and the pacific all sides had more or less appropriate equipment.