In my experience - having been a member of each there is an issue with both.
Having their own patrols they will first try to reach you with those before giving up at busy times and sending out a third party to you.
I have had experiences where despite my telling them that recovery is necessary they have insisted on sending out one of their people to suck his teeth and say "you need to be recovered". We'll see who's available.
Sat in the snow for 3 hours last year while that little pantomime played out!
Maybe check with your insurance company to see if breakdown cover/roadside can be purchased in addition to their cover fee. I did save a bit when doing this.
I am currently using 'Green Flag' and have used their services twice in 5yrs. On both occassions service was quick and both problems solved. I have everything except 'Homestart' and I feel the price is very competitive with the AA/RAC
TTG has a good point with checking with your insurers, there are some good offers out there.