And conversly, if you are the "I just want a great home theater system, and don't want to be bothered with all that technical stuff" person, then the JVC is likely perfect for you. Get someone to install it, and bingo - a killer picture, no fancy adjustments to make!
Computer users - look out! As mentioned, the JVC RS1 and HD1 have no good way to input a standard analog computer signal. The good news, is that if you have a Mac computer, you've probably got a DVI (HDMI compatible) output, and can output your computer that way to the JVC. Some of the higher end laptops and more powerful PC desktops too, are sporting DVI/HDMI, but certainly not most. So, for the rest of you, if you want to interface your computer to the JVC, you need a plan. The good news is that all you have to do is throw some dollars at it. There are several ways to go. Adding a graphics card to your computer that has DVI/HDMI out, or buying a converter box (a couple/few hundred dollars). Since the JVC is so much less expensive than the Sharp, even if you spend $300 (about the maximum) to solve this problem, you are still spending far less. So, while the Sharp is better in this regard, it shouldn't be a deal breaker.
More on interfacing: The Sharp also just has more inputs and outputs than the JVC, in fact, it is exceptionally capable. On the home front, with the JVC you are more likely to need a current AV receiver so you can switch between all your digital sources (ie. cable or satellite, standard DVD player, hi-def DVD player, and maybe a computer with digital output. The Sharp, on the other hand, has enough inputs that few would even need a receiver or other switching solution, to handle all the sources you have. (Either way, you need an AV receiver for audio.) As an example, my older THX certified Marantz receiver has only two DVI inputs and one out. With my digital "footprint" (cable box, DVD player, Blu-ray DVD player, HD-DVD player, and digital computer output), the combination of my Marantz and JVC's combined switching wasn't enough, so I bought a $200ish HDMI switchbox. In all fairness, even the Sharp and my Marantz would have come up one HDMI short, unless I went to analog for my laptop.
OK, I'm starting to repeat too much from the previous pages and the individual reviews. Here's how I see them stacking up, overall.