To try and understand whether neutering will affect behaviour you need to understand the impac testosterone has on confidence and aggression.
Testosterone lowers the threshold for aggression - it means the dog will use aggression at lower levels of provocation than he would if he had less testosterone. So, from that point of view, neutering lowers testosterone and therefore should lower aggression.
BUT
Testosterone also increases confidence. A confident dog may cope wit situations better than an under confident one and so be less 'provoked' in the same situation. This would mean that neutering a dog is more likely to leave him feeling provoked and therefore increase the chances of him feeling like aggression is his only way to avoid the situation.
If your dog is already confident and aggressive then neutering may help.
If he is under confident and aggressive it may make him worse.
Obviously, there are multiple complex variations whenever you are looking at behaviour so life is never as clear cut as above, but it gives you the guidelines.
In my opinion, if the dogs are drawing blood they are really meaning to fight. Just neutering is not going to be a magic wand. You need a good behaviourist in to help you.