You didn't say what sort of genny you have so none of this may apply to you.....
I did...sort-of
Mine is an Onan, not very loud in the big scheme of things but it's an annoying sound in my opinion.
I installed an Onan optional part they call a resonator I believe. I ordered it and was disappointed to find that it was an open flow through design. I went ahead with it anyway. The OEM muffler is inside the "box" with a tailpipe coming out with two 90 degree turns to get it outboard. I took the exhaust pipe to a local muffler shop and had them weld the resonator into place, and at the same time weld up an adapter bushing for a store bought Genturi pipe.
I don't remember specifics, regarding the empirical measured sound difference. I'm sure I posted it and if I can get some time to find it I'll post a link to that thread... but summing up as I remember it.
The dB levels as measured on my phone and not a "real" instrument were affected, but not by anything significant.
But the quality of the sound changed. It sort of mellowed it out a bit, made it ...well a tiny bit more pleasant for the lack of a better word. It wasn't a significant change.
Incidentally I say that the Genturi, when installed, has a similar affect, and it is accumulative. Together it's really an almost negligible change but I'd say it is different.
Many folks will tell you that the mechanical noises are more significant than the exhaust noise. That is likely true...but I would argue that if the exhaust noise was eliminated completely the result would be a significant improvement.
Before I did this I considered finding an automotive muffler that would work. I didn't look very hard but I didn't find anything. Then after I had done this, I found a tractor muffler at a Tractor Supply store that was about the same size as the Onan resonator, but not an open flow through design like the Onan part is. I'm fairly certain it would be better.
here's a couple photos of my install, and one of the muffler in Tractor Supply
edit: one more thought I've had was maybe trying to wrap that whole pipe and resonator with header wrap. i don't know what the real name would be. I read a post by someone, I don't know where, but they had said they did it more for the heat issues, but did see some change in sound levels... I'm guessing it would be a small affect too.