I think everyone is getting tripped up on noise reduction vs. decibel rating at the ear of the shooter. Forget noise reduction entirely, that is only happening with a can. What the OP is asking about is a muzzle device that directs more of the noise away from the shooter.
Any flash hider (FH) is going to redirect the report away from the shooter very slightly vs. a bare muzzle. Among muzzle attachments, about the only FH's I'd imagine that could improve on that is the old Vietnam era style XM177 FH, but it's 5.5" long, or the Noveske KH3 (Pig), but it's heavy.
XM177:
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Pig:
Then you get into compensators. They usually do little to hide muzzle flash, but mitigate perceived recoil instead. Almost all comps are louder than a FH or bare muzzle to the shooter. If it has any ports to the side of the device, it's going to be louder (even the ones on the page you linked). There are however three or four linear compensators that don't increase the report at the ear.
The oldest design is the Levang Linear Compensator.
Black River Tactical has one they call a cross between a comp and a FH. My cousin has one on his 18" 6.8 AR and it's pretty decent. It's also the same size and weight as the A2 "birdcage" FH. If you want some flash suppression and redirect of the muzzle blast, this may be your best bet:
I have a 16" 6.8 AR and I went with the Kies Blast Master from Joe Bob Outfitters. It seems quite effective on both report and felt recoil, at least for a linear comp that is:
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Notice it has a larger expansion chamber than the Levang or Black River, along with a shroud extending past the ports to direct the muzzle blast forward. Here's a couple of comparison pics with the Kies between some popular muzzle devices:
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They run $45 from Joe Bob and are available in 1/2X28 for 5.56 and 5/8X24 for 6.8/.30 Cal. All I can say is I'm happy with mine. Hope this is helpful!
Thank you. Your response was helpful. The only flash hider I have ever used is the A2 style. I was curious is others had a favorite style and if so why? If they do something besides make the rifle look cool, I was thinking about replacing mine. I knew of several makers that marketed devices that would reduce muzzle rise and supposedly reduce the noise. I was curious about the supposed noise reduction, defection, redirection, whatever you want to call it.
Thanks again.