With this sentence
What better way to celebrate the peace than with a fight?
Is "what better way to" an informal phrase? Would it be better to write
What is better than fighting as a way to celebrate the peace?
With this sentence
What better way to celebrate the peace than with a fight?
Is "what better way to" an informal phrase? Would it be better to write
What is better than fighting as a way to celebrate the peace?
What better way to celebrate the peace than with a fight?
This phrasing highlights the irony in the statement (a fight celebrates peace) by juxtaposing the words in close proximity.
"What better way" is an English idiom which is rhetorical. The question doesn't literally ask for a better way, it posits that there is no better way. I don't feel the idiom is particularly informal, I don't think you should worry about using it in formal writing.
What is better than fighting as a way to celebrate the peace?
This phrasing sounds needlessly clunky, and comes across sounding like you are seriously asking for a better means of celebrating the peace, since fighting is clearly not sufficient.
In studying the phrase "What better way", I have found that it is a commonly used phrase since edwardian times in English jargon and is considered proper when followed by a validation. "What better way, than to jump in head first".
What better way ... is elliptic not for What would be a better way ..., but for What better way could there be ....
The sentence (question) you provided is a part of some conversation or writing, and seems like it should be understood in some context.
To me, it seems something (at least) deviating from the actual discussion. Such things/feelings/opinions should normally be short so as to not disturb the pace and intensity of the discussion that was already taking place in conversation/writing.
The second sentence or question seems better grammatically, but like Jon Hanna I think it is too formal.
I think there are two ways you can put it in writing: