I own several of the JP Recoil Eliminators, including one on a 16" PTR91 I had custom built.
They are large but they all work exactly as advertised and truly eliminate the recoil to your shoulder. On .223 guns the sight literally never leaves the target so 50yd double-tap head shots are easy and 100yd double-tap body hits are virtually guaranteed. Put the cross hairs, or dot, onto the target and press the trigger twice. Your hits will be there.
On my 16" .308 the recoil is reduced that about that of a .223 and all muzzle climb is eliminated. That said, the bark is quite rude to anyone not directly behind the stock of the gun. One of the owners of CMMG said it felt like his brain "reset" every time I pulled the trigger.
Plain and simple, they work.
The Bennie Cooley brake that Stubby mentioned above is also designed and made by JP so I have no doubts whatsoever that it works well too. BTW, it was designed solely to meet the USPSA's Limited Class rules, otherwise the top guys would still be using the Recoil Eliminator "tank brakes" that they were all using prior to the addition of a rule limiting brakes to 26mm diameter for "Limited" guns.