Difference between 生气 and 愤怒
In terms of degree of anger, 憤怒 is higher 生气.
In terms of context, 生气 is usually used in colloquial context, whereas 憤怒 is usually used in formal context.
Another term you may be interested in is 抓狂, which is a colloquial term with degree of anger higher than 憤怒
Here is an interesting joke that can hopefully help you understand better.
I have quoted below the key phrases that denote the difference (forgive the offensive language used):
生气

「X的，神經病。你去死好了！」
&quot;F***ing psycho, go to hell!&quot;

憤怒

「你欠扁是不是？妈的，要是再打来，给我试试看！」
&quot;You want some beef? F***, I dare you call again!&quot;

抓狂

「他妈的！去你老母！你娘卡好！」
&quot;F*** your mom!&quot; (three variations with the same meaning)