One thing to be aware of, it may vary some by company, but even the "big" places often are really local. Hertz specifically franchises the name and allows access to their system for vendors, but that is about it. If you have a problem, and call Hertz, they will just refer you to the local guy, and all problem resolution will be between you and them, not Hertz.
That said, there are conveniences with using a big company, especially if you use their app and have some level of status. With local places, you just need to do some looking, you are doing a major transaction with someone you know nothing about. Most of the time there will be no issues, but it is always that one time we hear about on discussion boards.