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Does the cannon value affect the result of air-to-air fights? And if so, how important is the cannon value compared to the anti-air value?

I believe a hit determination is made first, using the air combat and experience ratings. Then if a hit is made, the cannon rating is compared to the durability to see if it is damaged or destroyed, based on a random number in some way. I could be wrong on this, but I think that is how it goes.

So if you compare for example the La-5FN (aa=23, can=5) with Yak-7b (aa=20, can=8), is the La-5FN considerably better or only slightly better?

For air superiority, or fighter against fighter, you typically want the better air combat strength. The higher cannon value is great against bombers, especially the bigger ones, where the small cannon values won't get many kills.