Both have two HDMI inputs, and both support HDMI 1.3 with Deep Color (not all projectors with 1.3 HDMI actually support Deep Color, for example, the two Sony's - the VPL-VW40, and VPL-VW60). Note, my older JVC RS1 is HDMI 1.2, and therefore lacks Deep Color support.
Both are three panel devices, with the Epson being 3LCD, and the JVC, being three LCoS panels (which they call D-iLA panels, just as Sony calls theirs SXRD).
Both have very good remotes. I like my JVC remote, but like the Epson even more. Both remotes have good range.
Last year, the JVC DLA-RS1 almost universally received rave reviews by reviewers (myself included), and owners. When it comes to sharpness, however, the JVC was just average when it came to image sharpness. I know, it was a major consideration for me, when I was deciding on my "next" projector, back in March of last year. I did decide it was sharp enough, and haven't regretted the purchase decision at all. Mind you were are not talking large differences, but subtle ones. Most likely if you saw the JVC at one place, and then one of the sharpest 1080p projectors at another, an hour later, many people wouldn't notice any difference.
So, my point is, while sharpness varies on 1080p projectors, it doesn't vary much. The worst of the 1080p projectors, when fed 1080i or 1080p content will still be immediately sharper than the sharpest of the 720p projectors, and the difference will be far greater, than when comparing different 1080p projector models.
So, how does the JVC DLA-RS1x stack up against the Epson? First, remember, that I have not yet received an RS1x for review, so my assumptions here, and in some other areas, are based on the RS1 that it replaces. In this case, it's the same lens, lens shift, etc., so the two should be essentially identical.
And that means the JVC is a little soft compared to some of the competition. That competition definitely includes the Epson Home (and Pro) Cinema 1080 UB. I find the Epson provides a slightly sharper image, yet it is definitely not the sharpest in class, several other projectors being better.
How great a difference? With casual viewing you are not likely to notice. When viewing hi-def movies (Blu-ray), the difference is very slight, because there's a lot going on, due to the content starting out on film, with film grain. In most cases, if I walk back into my theater, and look at the screen, I'm just not going to be able to use sharpness as a way of telling whether I'm running the Epson or JVC.
HDTV hi-def material is a little different, as the best of it (production qualities, not content), is now being shot with digital camcorders, not film. That means no film grain, and a perfect one-for-one pixel mapping (if overscan is off, and you aren't using keystone correction). With content like that, from Discovery-HD and other channels, the difference is definitely more apparent, but still just a small difference.
I'll definitely give the Epson the advantage, but, from my own experience, the difference in sharpness, is going to be a very minor issue, and not likely to affect the final buying decision.