The US Travel agents cannot always give any extra discount on RCI whereas UK Agents can usually offer a % off RCI on line prices. However I have booked using US Travel agents who will price match any Uk quoted price by giving the difference in OBC. The US Travel agencies are great for last minute bargains but remember its Cruise only and there are some lines they are not allowed to sell to UK such as P&O. The one distinct advantage of booking with US Agent is that your deposit is fully refundable should you need to cancel prior to balance due date. They also are very good at switching the booking over if the price goes down, to match the lower price.
I did reply yesterday but I fear it got 'booted' by the moderators, so just a few points to add to Bradbury's. P&O, Princess, Cunard are no no's & some unscrupulous TA's are taking these bookings from UK customers, only to find themselves in difficulty at check in!, so like everywhere else, cowboys operate. The well known reputable agents are no different to phoning a TA down the road in this country. RCI, Celeb, Carnival, NCL, no problem. The main savings are on American departures(Caribbean) & less, if any, on European sailings. Finally as Bradbury stated, you book your own flights, transfers & hotels, which is no big deal & something I do regardless, whoever I book with as I don't enjoy the herded sheep scenario.
I should add. If you see a wonderful, super cheap, late deal in say, the Caribbean, just can't believe the price, be aware you be very unlikely to get a cheap or even reasonably priced flight ex UK, to get you there.
We've booked our last 10 cruises through the US - have never had a problem and always saved hundreds of pounds, but be aware you take a risk with the exchange rate. If the recent drop in the pound continues, you may get an unpleasant surprise when the balance becomes payable.