OK, the basics – the Epsons are brighter at maximum, but calibrated the JVCs are at least as bright (brighter than an Cinema calibration on the Epson about the same on a Bright Cinema calibration.
I’m going to use the Home Cinema 5040UB as our example, rather than the 6040UB, because the 6040UB is bundled with enough extras (longer warranty, cable cover, spare lamp, and ceiling mount) to make the price slightly murky, depending on what you value those accessories as worth to you.
That technically makes the JVC the more expensive at $3999 vs $2999 – it does have a longer warranty (by one year) than the HC5040UB, but lacks the two years of (virtually) overnight replacement program for warranty issues.
Update: April 2017: Epson just announced a price drop on the Home Cinema 5040UB to $2699. That further separates the two in price, and for some, will make the decision between these two great projectors, a little easier (and for some, a little harder).