I have had H1 with Phase Back, H2 with same Phase back, H3DII-31 and H3D-39. Going from H2 and Phase back to H3 with integrated back was a huge leap forward. Having two manufacturers and two batteries in the same camera was a pain. Next will be an H4D or H5D with True Focus.
Of course the other side of this argument (that a P1 back is better on an H than a Hassy back) is supported by the overwhelming domination of H2+P1 in the rental, production, and digital tech markets during the era that the H3D was current. It was the most popular combination until around the DF+ days.
the only issue I have with running an H1 with a P1, is that I cant update the firmware on the H1 without a hassy digital back (or sending it off and paying someone else to do it)
I don't know where you are located but as a Phase back and Hassy body/lens dealer we do H body firmware updates as a free service to any of our clients in NYC and LA and Denver (or anywhere for the cost of shipping).