I've been with both, but have only ever had to call on the services of the AA. I'd say firstly, do a good comparison on their web sites for their like-for-like new member rates. Once you've taken out cover, I'd recommend logging in to cancel your "auto renewal", or at least make sure it's not active.
When your renewal quote arrives next year, sit down before opening the envelope. They reward your loyalty by putting up your renewal premium. This year, my RAC had increased by about £37 from last year, with no call on their services. The current RAC new member rate is around £63 - I was asked for nearly £250 to renew. If you phone to query the renewal cost, they'll probably do the fake "I'll speak to a manager" routine and then offer to reduce the fee by a small amount. This may be repeated a couple of times.
For renewal, check the other organisation for their rates and swap one to another if you're not happy with the quote/s. You could always scare them by asking if you let your cover lapse, how long must go by before you qualify for their new member rate. The AA told me 8 weeks. For years I simply alternated the RAC and AA from one year to the next, to get the cheapest introductory rate. Good luck!