Мы будем помогать друг другу всем.
I wonder how placing "всем" after "друг другу" compares with:
Мы все будем помогать друг другу.
Is it just a stylistic difference, or are they nuanced?
First phrase has the meaning of "we'll be helping each other with everything", where everything refers to the amount of help they can provide each other, i.e. "with everything we've got, we can spare, etc." Note that if you wanted to mean "we'll be helping each other in everything", you would use
Мы будем помогать друг другу во всём.
As mentioned by Баян Купи-ка in the comments, всем in the first expression is the instrumental case of всё. Adding чем сможем at the end can help with understanding why the instrumental case:
Мы будем помогать друг другу всем, чем сможем.
Regarding чем сможем vs чем можем that you asked about in the comments, there's literally no difference in meaning -- a native Russian speaker would interpret them the same way, at least in the setting that you provide -- but formally, всем, чем сможем is "with everything we'll be able to spare/we'll have" and всем, чем можем is "with everything we can spare/we have".
Second phrase = "we all will be helping each other".