I can't really comment on the other agent that you have detailed as I have no experience with them, however I did sell my flat (yes really) through Hamptons late last year. Like all agents they have their good and bad points, there was definite foot traffic through the flat (some 20-30 viewings) and I believe that they get good hits on their website via Primelocation and Rightmove etc. They do give you reports on the hits your property has received.
However they state that they will call you for a "Hamptons Tuesday" every week to update you on what is happening with your flat and similar properties but this maybe happened proactively 3 times in the 4 months they had our property. That said we were talking fairly regularly at my instigation to get feedback on viewings, some of their team were better at calling you back to give feedback (as I had requested it after every viewing) others were not. That would probably be my biggest gripe, the communication could be very slow, with non-returned phone calls, which I found to be very frustrating. I also got very little notice of viewings so you have to be prepared to live in a showhome environment which does take daily effort. However their advice on the market wasn't bad, and they encouraged us to hold out and not accept some of the stupid offers people chanced their hand with, they also didn't constantly badger us to drop the price but did advise us when similar flats had done so, and ultimately the flat was sold at a price we were happy with.
My only advice would be that whichever agent you go with you need to stay on top of them to make sure your property is a priority, and see if you can get any leeway on the percentage they charge as it is ultimately just a very expensive property dating agency. Most of the procedural stuff was undertaken and chased by our solicitors.