I rent 3 or 4 times a year in the USA. I almost always go with Avis or National, and the differences seem much more location and 'random that day' than any consistent difference. I rent 3 or 4 times a year in the UK, and almost always choose National as the location suits and mostly the prices have been fine. I used to use Thrifty and after that Hertz, drifted away from Thrifty when I didn't like their toll policy in Florida, where avoiding cashless tolls became too hard if you're a non-expert in local road knowledge, and stopped Hertz as I've not found a competitive price from them in years. I'd honestly go with price unless you have real issues with a particular location. My next two USA rentals are National, as my last two Avis ones have been high mileage vehicles, presented as upgrades, but who really wants a Explorer XL Max as a solo traveller. I guess I do like the aisle setup at National and having some choice. Almost all my rentals are large airport ones, Tampa, Miami, Los Angeles, Las Vegas, Seattle as examples, I guess smaller off airport locations could be quite different.
I've not had any disasters with any of these companies, a few to and fro's about existing damage or new, bit that's been at city/downtown returns, but I always try to get a close out receipt before I leave. I'm aware they have your card and what can happen later is somewhat uncertain.

I'm interested by a few recent posts I've seen suggesting these companies have particular levels in the market. I (thought I) knew Thrifty like Alamo was budget, and that Avis and Hertz were premium, was uncertain about National. Interested to see comments around Avis/Budget being so similar, which means the brand division is sort of pointless, and National being presented as higher end.