The only difference would be that some people insist that you should not end a sentence with a preposition. (This has been asked both at ELU and here on ELL.)
Those people would consider the sentence "What are you going to die for" wrong.
However, it is very common and widely accepted to end a sentence with a preposition, so both sentences are fine. Just be aware there will be people who consider the "for what" as "better".
Sometimes, not only in English but in all languages, we want to emphasize certain situations. And then the language itself gives us devices that aren't always common, but we use them anyways, based on known and meaningful expressions.
I am very hungry
We can depict that the subject has surpassed the status of just "hungry" for they must have stayed a long time without eating. This is a known meaningful expression.
Murder is very illegal
From this, even if it doesn't make much sense in the binary nature of the word "legal", we can depict that "murder" is a crime that, morally or ethically, has surpassed the status of "illegal".
We can state that by looking at another not-so-serious crime:
Parking on the sidewalk is illegal
Yeah, we all know it is illegal and wrong. But it is a petty crime compared to murder. In some countries murder is penalized with life imprisonment, even with death penalty, while parking on the sidewalk gives you a fine and, in the worst of the cases, your car is towed.
We can still say that "Murder is illegal", of course it is, but in the sentence, the "very illegal" was made to emphasize.
Best Answer
This is what I copied from Quora:
Here are some points from the "Difference Between" site: