At 6 to leave him out in this way is horrid. By doing so, you and your son are now the bullies. Your behaviour will be noticed by all the other parents so expect them to have an opinion of you which may not be great after the event. I would think you were nasty. It's not like they are older, he is 6 years old.
You can easily manage the situation, talk to the other boys parents, tell them you are in a pickle as the boys don't get on ( are they aware of the fighting?) but you don't want to be a nasty vindictive person and leave him out at a party, so maybe they could attend to supervise? Or maybe they are happy for him not to attend and they can monitor his behaviour a bit more?
It's an excellent opportunity to teach your son about managing relationships, behaving to others as you would like done to you, forgiving but also how to take control and not stand for abuse.
I don't believe a 6 year old is a fully formed bully for life, but not managing relationships and the 'eye for an eye' attitude will not help in the long run. Your son may have years ahead with this boy, do you want the relationship to always be awful or could you help the situation and teach your son how to help himself?
Hope he has a lovely party regardless.