Tough question. I believe it depends on the level of both as far as what pisses me off. Although I know the definition of both words I will attempt explain based on a dictionary's definition of both words:
ig·no·rance (?g'n?r-?ns) pronunciation
n.
The condition of being uneducated, unaware, or uninformed.
stu·pid·i·ty (st?-p?d'?-t?, sty?-) pronunciation
n., pl., -ties.
1. The quality or condition of being stupid.
2. A stupid act, remark, or idea.
But in order to understand stupidity, I must understand what stupid is. Excuse my analytical habits, it is how I operate:
stu·pid (st?'p?d, sty?'-) pronunciation
adj., -er, -est.
1. Slow to learn or understand; obtuse.
2. Tending to make poor decisions or careless mistakes.
3. Marked by a lack of intelligence or care; foolish or careless: a stupid mistake.
4. Dazed, stunned, or stupefied.
5. Pointless; worthless: a stupid job.
Ignorance is pretty straightforward. It simply means "I don't know." or "I am unaware." I find this acceptable. As humans we are ignorant, there is plenty that we don't know. And that is fine, because it gives us something to look forward to learning. But this is where ignorance pisses me off. I'll dub it stubborn ignorance or hell...bigotry. "I don't know or I am unaware but THIS is how it is even though I have no empirical evidence or sensible explanations because I am right and what you say is wrong/stupid/etc." THAT is where ignorance pisses me off. Being ignorant and not bothering to cure it while one pushes their opinions onto others and declaring others wrong or stupid with little reason. Even worse are the ones who embrace bigoted ignorance like a badge of honor. One who refused to admit to their faults and mistakes. I hope that explains ignorance in my opinion.
Now onto stupidity. As most of you who know me or remember me, I have a low tolerance for a stupid person. Mostly ones similar to the bigoted ignorant above in which I would consider stupid. But let's use a few of the definitions above. When someone is obtuse but is trying, sure it may be annoying but I give the person some credit for trying to cure themselves. Some people just cannot get the gist of something as quick as others. Even I have my "stupid" moments. Which is why you'll never see me engage in politics. All that terminology pretty much eludes me even when explained. To me politics is a bunch of name tossing. In any case, the obtuse person that tries isn't THAT annoying.
Tending to make poor decisions and mistakes, well that depends too. Depends on the severity of the mistake. The worst things imaginable can be done with the best intentions. I believe Alan Grant from Jurassic Park 3 said something like that. If you want to save the whales from extinction so you spend tons and tons of money trying to rescue every beached whale (which apparently costs a lot of money for equipment) and you become broke, well that is stupid but at least it is something you could recover from. Now if you try to save the whales by trying to kill every animal that attacks whales, well that is just straight up stupid beyond belief and you've become a walking disaster. I'm sure I can think of better analogies but you all get the drift.
Marked by a lack of intelligence or care. THIS IS PROBABLY THE WORST. This right here is where I cannot stand stupid people. When you are an idiot and don't care and you exist only to spread your stupidity and hostility like a virus I deem you unfit for breeding and I desire your eradication from the gene pool. Darwin Award winners are a perfect example. Need I say more? Fucking morons.
Being dazed or stupefied happens. Nothing really special. We all take that stupid pill at times, it is people who are stupid for most of their life that are the real danger.
Pointless and useless. Rapists, murderers, and most politicians. Need I say more.
I must admit, there is one more group of people who either fit in or outdo stupid and ignorant people. And that group are...The Delusionals. And in America, it is the deadliest disease ever. I'm sure a lot of you agree.