I have both. The 9mm JR has worked flawlessly for me as has the CX-4.
A few things to consider:
The JR accepts a lot of AR-15 parts including stocks, handguards and the trigger group so you can pimp it out as much as you like. The CX-4 is what it is. There's not much you can add to it if that's your thing. Both use 10 round pistol mags. The Glock mags for the JR might be a bit cheaper than the CX-4 mags.
I found the above comment about the JR trigger interesting

as the CX-4 stock trigger is far worse (probably 8 pounds or more).
Unlike the CX-4 the JR has a lot of metal parts (receiver, handguards, buffer tube, etc.). The CX-4 is pretty much all synthetic except for the barrel.
The JR is far more of pain to clean as you have to remove the stock to get the bolt out. Not a tough job but more labour intensive than the CX-4.
Accuracy wise I haven't noticed any significant difference.
The original JRs had some teething problems, particularly with the 45 ACP versions. These seem to have been resolved, however. I personally have had no problems with mine which is a Gen 2 version. I can't speak from first hand experience but most posts on this board indicate that JR is a good company to deal with and quickly resolves customer service issues. I can't recall seeing any posts about Beretta service. Maybe someone more in the know could chime in on this.
Al Flaherty's had a great deal on the CX-4 at $999 (that's when I got mine) but the price has gone up so now you're looking at about $1100 which comes in around $150-$200 more than the JR. That buys 4 or 5 mags or a lot of ammo.
To be honest I think either one will make you happy. They are two quite different animals so appearance and your personal taste are going to be a big consideration in which you choose.
Just my 2 cents.