If you don't notice the sharpness difference too much, you should definitely get the JVC. The x5900 is a lot of bang for your buck. Even for someone like me who prefers the Sony image it was a difficult choice.That's a very nice comparison video, and I think the difference in sharpness between both is pretty obvious in this video too.
Just a question about your needs:
1. What kind of screen size are you lighting up?
2. What kind of sources are you using? TV? 1080p blurays? Games?
In my opinion, the Sony is superior in picture quality because it's just a much sharper projector. It has a best in class upscaler making your TV/1080p material look amazing that JVC does not have, and true native 4k materials are that much more impressive (imo a big difference as you can see in the comparison video).
However, there are on this forum, that prefer the black level of the JVC, which is superior. It's what you prefer out of your projector.
Also, the additional arguements of high brightness and reduced cost for the x5900 are good ones. You should see if you need the high brightness and if you're OK with paying the extra.
Sitting at 10 feet, on a 114 inches screen, in a dark room painted dark blue.
My only source will be a Blu-ray player, no download or gaming for this old Cat.
In a few spot, I did notice that the Sony was a little bit sharper, but on most scene, the JVC was my preference.
But must admit than I am more, an audio guy than video, therefore, I might not notice what some other do.