I'm not sure what the difference between a 57F710S and my 57S500 are, but I can tell you that Hitachi makes a heck of a set.
Mine will do PIP. THe 57F seems to support 8 PIP's and compu-cards(Like PCMCIA adapters for picture slideshows or something).
THis mitsu... You get 8 more inches and only PIP mode but the prices are nearly equal...
I would go back and actually take 30 minutes and get the feel of each remote. See if they have it hooked to a live HD feed. Take the brightness down to 25-30% and set everything else to around 40.
I'm not sure who makes the color guns for the mitsu, but hitachi seems to make better optics.
Whichever feels better in your hand and is easier to control would be my pick.
I gave $2700 for mine in Nov 2003.
Take the plunge. You won't be sorry.
Mark