Hi Nina,
I can only answer based on my own experiences but I prefere an independant.There are several reasons for this.
I have always tried to get to know the lady...and no, I'm not prying into their personal life, but getting to know them as a person. When you know and like someone everything else is better, independant's seem to have the time and inclination to go this route.
Then there's the monetary aspect, I prefere to donate my hard earned dollars to the person providing the service and not a third party, who in this instance is often a sleazy pimp-like creature that instead of getting off of their oversized derriere and earning their own way, would rather make money off the labours of others.
Then there's the safety aspect, here an agency can be useful....the idea of going to meet someone new must be very daunting, so having someone looking out for your personal safety is probably comforting.
Lastly there's your own comfort level, spending a few bucks on a website and cellphone is a small investment that allows you to screen your own client's, work only when you want and see fewer client's thus providing a better service, also making for a happier clientele.
Safety should alway's be formost on your mind and having a network of friends who know what you do can accomplish this.