I would go for AVG, Norton's popularity means it's also the one most malware is designed to get around.
AVG runs faster because it takes up significantly less resources to run, something important if you're looking at software that will be constantly running in the background, like an anti-virus.
While I can't comment on Norton's features, as I havn't had an in depth look at it myself for many years now, I have used AVG many times and the free version is not lacking for features.
Norton will probably provide customer support however, which judging by your question you may need in the long run. How long is the Norton subscription for anyway? The last PC I bought retail came with only a free 2 months.
Also keep in mind that if you choose to stick with AVG, you'll need to download a special tool to remove Norton in it's entirety from your system.
Actually, if they're offering Norton, I'd take it over AVG Pro. AVG free edition is the best free antivirus, but Norton 2011 is winning in the non-free category this year in terms of preventing infections and cleaning them up.
Source? I've known companies to claim similar things despite often being in the bottom rung of quality, and I would be suprised if this was actually true.