JVC DLA-RS20 vs. Sanyo PLV-Z3000
I'm not going to say much here. Because of brightness differences, and black level performance, these are not even close to being competitors. The Sanyo PLV-Z3000 has the weakest black levels of the top of the line "ultra high contrast" LCD projectors, so while still very good, their black levels are no match at all for the RS20. When it comes to brightness the Z3000 is actually a little brighter in brightest mode than the JVC, but the JVC has roughly double the lumens in it's best mode, when both have their iris's open.
The Sanyo is a really good projector for the bucks, and has a three year warranty, but the only time someone might seriously consider both, is if they are torn between spending a little now, and planning a major upgrade in a year or two, and they are a smaller screen user.
JVC DLA-RS20 vs. Optoma HD81-LV
It's probably been two years since we reviewed the HD81-LV, so I'm relying on notes and the HD81-LV review, more than memory.
The HD81-LV is a screamer - brightest single chip DLP around, and brighter than the JVC in any comparable mode. Got a really big screen, and if you aren't a "purist" the HD81-LV pops and really wows you. I do remember my first impression once I had it properly set up. It was something like "finally a projector that looks good, and doesn't even consider my 128" screen to be a challenge. Its colors are rich, well saturated (though sometimes over the top), and have good depth. The JVC is simply far more refined an image, not quite as bright.
When it comes to black levels, the Optoma is a typical Darkchip3 DLP projector, and no match for the RS20 (and for that matter the RS10). Optoma HD81-LV owners will, like RS20 owners, want to get their projector properly calibrated. Want that 150" diagonal screen, start taking a serious look at the HD81-LV.
Price wise, street on the HD81-LV has been hard to track but it definitely should be findable for a bit less than the RS20.