I think both have pros and cons, but overall I've had the best service from independent escorts. I think when the girl is working for herself, she's more invested to provide a good service.
Having said that, some agency services are also good at implementing standards across all girls, so even though you probably wont get a really great service, you're also less likely to get a bad one.
The best thing is to find a girl you like, private or agency, and stick with it. I've often found the service gets a lot better too over time as you become a regular, especially if you click with the girl.