The big problem with escorting in the US is that - outside a few brothels in rural Nevada - prostitution is illegal for both client and escort... and guess which one is more usually targeted.
In the UK, agencies are breaking the law but the individual escorts aren't; there, you are trusting someone nowhere near where you are that you are not going to someone looking to arrest you.
Now obviously, this does not stop either agencies or independent escorts existing and it is possible to reduce your chances of ending up in handcuffs: doing your own screening being one of the big ones.
Do a search for 'New York' for some interesting threads.