I recently had a minor accident in a parking lot. I have Geico, and the other person had AAA. I was thinking of switching to AAA too before this incident, but after this I am going to stick to Geico. The people I dealt with from AAA during this process were not very friendly or helpful. When someone gets in to an accident obviously he/she is in distress, AAA agents were very insensitive to the whole issue.

I had a really good experience with Geico. Every agent I dealt with from Geico were really friendly and helpful.

On the good side, they sent me check within 2 days. They sent an agent to take pictures of my car, whereas Geico did not (b/c it was 50/50 case I guess). The lady was incredibly rude, and insensitive.
If you don't care about the service very much, and if the savings is huge it might be worth it. I don't know it's a personal preference. Personally, if that is the kind of service they offer, I would rather stick to Geico and get better customer service when I am in distress. If it was just one person, then I would not care, but I dealt with atleast 5 agents during this process and none of them were nice.

Good luck!