I currently use the RAC but that's mainly because I get a good deal through my car insurance. Their service is just as good as the AA, who I've also used in the past.
In my 'trade plating' days, delivering cars across the country, the firm I worked for had agreements with both the RAC and the AA to assist at breakdowns. I had to make countess call-outs, with five in the same week once (and with three of those being on the same day, to three different vehicles) and I could never see any real difference in their service.
However I've also used AutoNational Rescue in the past and been satisfied with their services. If I wasn't getting a good price from the RAC through my insurance, that's probably who I'd still be with with now:
https://www.autonational.co.uk/