Many people have preferences. You have to decide for yourself. I am fine with either one.

Do a search on this board there are many discussions on this question. If your search skills are better than mine (which isn't hard to do) you will find plenty.

For me the advantage of an agency is the ability to book on short notice. With references, you may be able to get screened with a minimum of fuss. The biggest disadvantage is the agencies tend to draw the attention of uncle Leo. I wouldn't be worried about the appointment, but them having my info should they get busted. So if you can get verified without giving your real name, then your risk is reduced significantly.  

Solo mis dos centavos.

I have seen ladies from agencies and who are independent. I find the agencies to be very consistent in the quality and predictability of the session. I prefer that consistency and trust.  
In Phoenix, however, the agencies have either closed/left or gotten busted. There is one reputable agency but the donation is expensive. I am not saying its not worth it. Its just more expensive than what the other agencies charged. So, now I stick with independent.
Either way, its very clear that we as hobbyists should be diligent in protecting ourselves. That means having burner phones, seeing only well-reviewed ladies/agencies, never giving information that could be come back to haunt you, etc.

Why bring third or additional parties into play?