I would bet, Avira would be more reliable than BitDefender... especially on W8.1 system.
BitDefender has better overall protection than Avira - because of web-filtering and Active Virus Control. However, a lot of users complain that BD does not function properly on their systems. Protections against malicious scripts is spotty at best. There is no firewall as well - a big security hole. Plus, you have to be signed into your BD Free account all the time for signatures. It uses little to no resources, but scans are really a crawl... something some users are not used to.
Avira is better than BD when it comes to speed, polymorphic detection, but it tanks when it comes to malicious scripts, protecting browser settings, Windows firewall and UAC. It integrates Windows firewall into the user interface... which helps the typical user not one bit as managing Windows firewall (WFwAS) through its interface is not easy for the novice. It can be a network hog if you use a metered connection. Avira is a very reliable advanced scanner. It works well on W8\8.1 and 7.
Signature wise - Avira and BD are about the same.
Reliability is the 1st priority... there is no use in installing a security soft and keeping it if it does not work on your specific system. I've tried both Avira and BD Free in the past. Avira worked, whereas BD Free conflicted with my system (supposedly BD improved W8.1 compatibility).
You're not going to know which one will work best for you, on your specific system, until you try each one out.