Well, I used both, as I used Norton in the past ,and regret it, and AVAST just till 3 days ago.
Now I have installed the AVIRA premium, wich use the same engine with AVIRA FREE PERSONAL.
As you can see here:
http://www.av-comparatives.org/seiten/ergebnisse_2008_02.php
AVIRA is one of the best on detection with a 99,6%, little lower from AEC trustport wich has 99.8% on DEMAND SCAN.
Demand Scan means, the scans performed in every day use of the computer from the resident scaner anti-virus load next to clock in taskmanager area.
AVG was lower wityh 98.1% but still GREAT results for A FREE Anti-virus and for a home user.
With the use of AVG Antispyware, or SPYBOT S&D wichj also FREE, you can have full FREE total protection.
And I emphasize to word FREE cause a user here called "Samuel Adams" willclaim that AVIRA or AVG will crash your computer (as you can see in his profile) wich it's TOTALLY A LIE.
Now about recources,
AVIRA resident (on demand scaner) use about 17MB of RAM, AVAST used ABOUT 34MB of RAM, and AVG used about 30 MB of RAM.
NORTON needed more tha 50MB of RAM and a 5 to 9% of CPU usage.
While they scan in the background (the time you're working with your PC ) CPU USAGE is about 1% to 2% for both Avira,AVG and AVAST.
FROM above 3 AVAST has the faster engine while make a full system scan.
In my system (I have two 320GB disk, and scaned ALL FILES) AVG NEEDED almost 4 hours, AVAST needed 2h54min and AVIRA needed 3h10min.
So choice is yours. ALL ARE FREE, ALL are among the best, with the exception that AVIRA FREE EDITION don't have activated the WEB scaner and E-MAIL scaner,(that means you can't scan e-mails the time you download them, or web pages ther time you visit them), wich are options only for premium version,
but this can be fixed with SPYBOT S&D and the teatimer scaner it use, wich u can download from here:
http://www.safer-networking.org/en/download/index.html
one of the best FREE anti-spyware.
Have a nice day