Kirk would have seduced the Female Changeling and stopped the war.
Picard would have been unwilling to put aside his moral code to get the job done and have failed.
Janeway would have been a flakey psycho that ends up initiating a Ferengi holocaust because she had period pains.
Bakula would have helped Weyoun realise his potential as a baseball player. He then leaps to his next body, hoping it'll be that last leap home...
Abramsverse Kirk would have been too blinded by lens flare and end up crashing the Defiant in to Bajor as a result.