As far as I've experienced, I can say that stamina has a significant impact on performance. It's hard to say precisely what the effect is, but you can see it in the game ratings for your player. A low stamina player will only perform with low minutes (1-3 stamina players can only play 30 minutes decently), when they play more minutes their perfomance drops significantly (ie he'd get 15.0 rating when playing below 30 minutes, but 12.5 when playing 40).
So what can you do with this information? Depending on your personnel, you can decide to train stamina. If you don't have very good subs, I recommend at least 5 stamina on your starters. More than 7 isn't too necessary unless you intend to play your starters more than 42 minutes. As said, it's harder to maintain gameshape if stamina is very high, because they'll play well above 40 minutes, meaning that 2 starts will result in too many minutes.