We decided to stay at the Portrait Suites and are very grateful for this recommendation here on FT (I doubt we would have found it otherwise). This is a special place that makes you feel as if you actually live in Rome. The rooms, service and location are brilliant. The rooftop bar (now fully open) is a heavenly place, and extremely private (only 16 rooms in the 'hotel').
This was a different kind of experience, and one where we felt we got what we paid for. We did look in the Hassler and the St Regis, and although I am sure they are fine hotels, we are ever so grateful not to have stayed there - they were just nice hotels. Portrait Suites is something special.
It is not perfect mind you - the breakfast was small and not special, the concierge service was poor (but I have heard more positive comments from others) and charging for internet usage in such an expensive place always gets me riled up. On the whole, though, I don't think I would stay anywhere else in Rome.
Thanks again to those who responded to our OP!