Thing I liked about the JP's.
Handguard Diameter
Action smoothness
LMOS (somewhat)
Overall build quality.
Then I hunted with one. The hand guard is frigidly cold to hang onto for hours in the Maine woods in November, Mine did not have the upgraded MU upper, and pine needles, leaves a shit managed to find its way into the rifle. Something about the shape of the Brake seemed to catch every twig in the woods.
Side charge--as much as I loved it at first, I found myself hitting my knuckles on my QD levers for my scope mount, accentuated with gloves on. The manual of arms just didn't fit me.
JP barrels---they are Wilson barrels that JP finishes. They are cryoed and somehow thermal fit. I was told by JP CS that I shouldn't remove my barrel to cerakote or dip the gun, as it will affect its accuracy.
LMOS/Adj Gas block--I personally had troubles getting it "tuned". I also ended up not liking the socket screw for adjustment.
JP Recievers--As far as I know are not manufactured by JP.
Things I love about Larue:
I have had nothing but fantastic experiences with Larue Customer Service.
I truly love their Predatar and Prodatobr rail designs. They fit my hand very well. I also like that they have the GAP panels, plastic is much easier to keep warm to the hand.
The fact they make their own in house barrel now, that are insane accurate. That are not "thermal" fitted.
They make their own lowers/uppers.
Their PST switchblock design for suppressor use. A simple left or right lever.
The complete takedown capability of the Predatobr.
Their trigger choices.
Use of non proprietary BCG parts in the 556 rifles.
Overall Build Quality.
Both Companies build a fine product, I proudly have a JP and Larue sticker on my Jeep.
These are just my 2 cents of why I switched to Larue and have not looked back. Their is a lot of bad info in this thread as others have mentioned. But I saw no one who posted their personal pro's/cons.