I had the Harbeth P3ESR a few years ago. I now have a pair of the current version of the Graham Chartwell LS3/5A. I haven't heard the Falcons but my Graham LS3/5As are much better than the Harbeths.
Like all Harbeths, the P3ESR have a slight plumminess to the sound; they tend to impose their own character on the music, regardless of amplifier.
The Graham LS3/5A are much more neutral, and much better at reproducing the distinct tonality of instruments accurately, while remaining dynamic, musical and engaging.

