Regarding Avira, I've run that on a number of systems and have never experienced any BSODs... until this event. Have you experienced issues with Avira in this regard?
The common issue is that AV's like AVG, Avast, Avira, etc. do not get along well with outdated drivers, so whenever someone is sufferring from BSOD's it's a must to replace his AV with MSE for 2 simple reasons:
1) MSE does not invoke BSOD crashes, almost never unless it is actually a hardware's fault
2) AV must be removed so one can update his drivers and do the necessary fixes without the frequently occurring BSOD's provoked by a notorious antivirus
So if your crashes are gone and you're reluctant to get rid of Avira, keep it. But if BSODs reoccur then remove and install MSE.