The excellent Sony VPL-HW50ES projector (pictures)
Apart from stellar image quality, the Sony has three main things in its favor: it offers a better picture out of the box; it has a better selection of included features including two sets of glasses and even a spare lamp; and it makes less noise in its highest lamp mode.
The only "negative" the Sony has is an almost imperceptible blue color cast, but only when compared directly against the more lush-looking JVC -- all of the Sony's colors are within an acceptable range.
Personally, I would be happy with either projector, as they both offer deep blacks, as close to reference color as you can get, and a great price-to-image-size ratio (not including the price of a screen). I'm going to push for the Sony because of the included extras, higher output, and relative ease of setup, but you could feasibly buy either: they're fantastic.
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The picture quality of the Sony can be summed up with one word: superb. While there were some oh-so-slight blue tinges to some colors, its overall color balance could only be described as excellent. Shadow detail was fine, and black levels were the best I've seen in a home theater projector. Both the Sony and JVC are capable of jaw-dropping pictures, and if having to choose between two very good projectors is your only concern, it's a great problem to have.