According to the latest av-comparatives.org test, AntiVir has a better overall detection rates than avast! but only by a small margin, for the most inportant group of malware (industry standard) so called ITW , avast! and AntiVir are equally good, according to some tests such as ICSA Labs and Virus Bulletin.
Whens it comes to free editions, avast! Home and AntiVir Classic...
As justin1278 said, it's just a matter of opinion and what you're looking for in antivirus software, in my mind avast! does outperform AntiVir in overall soluions.
For example, you can tell avast! home to checking for new VPS updates hourly when you're online but in AntiVir you can too but every 24 hours.
For me, detection rates are not everything when looking for an antivirus software but overall solutions (features, update mechanism, etc.) are the most important factor for consideration.