I've no experience with the Phil Jones gear, but I've used lots of various 'headphone rigs' over the years, and my current and last rig is a Mackie 802VLZ mixer and A-T D40fs cans. Especially with five-strings, most battery powered things would fart out, and little earbuds or WalMart headphones just added to the misery for me.
The Mackie's AC-powered, the Onyx preamps won't break up without a lot of ham-fisted knob-turning, and this sort of thing begs for good, studio over-the-ear headphones for me. The D40's are a minor studio staple, and the Mackie has a 1w headphone output, so it gets plenty loud. I only use this to practice along / learn new tunes from pre-recorded stuff, so for playing along with stuff it suits me personally.
Of course the tone is that 'mixer dry' sort of sound, so you could sub one of the FX Mackies instead or insert pedals or a tube preamp on the way in to get more of an 'amp' sound.