There is more to this.
A lot of the noise in a GA plane is from the exhaust, but very much is from the rotating prop slipstream which hits the cockpit all around and vibrates the cockpit material.
I have recently done some measurements on this.
The engine fundamental frequency (crankshaft rotation) barely features - except at idle. The piston frequency (6th harmonic of a 6-cyl) does feature but not strongly.
Most of the noise peaks at mid-range (~ 250Hz) but is otherwise quite broadband and ANR headsets can and do work well on this. There isn't much (on piston planes) into the kHz range, on which ANR doesn't work and only heavy passive attenuation would be much good.
The Bose X headset is suprisingly, after all the years, still the best. There are suggestions that the Lightspeed Zulu (never tried it myself) is close though. The rest of the 'pilot shop' headsets are pretty poor compared to the Bose X.
Another issue is that ANR headset attenuation is heavily misrepresented in the adverts. Bose carefully avoid making any db claims in their adverts. Others, notably Pilot Industries, make various claims like "22db additional noise protection" which suggests their ANR gives you another 22db, which is rubbish - it's 5-10db or so. I had one of these and eventually sent it back to Pilot on grounds of the ANR barely working and the mfg confirmed it was to spec. The Bose ANR is very much more effective though. Sadly you get what you pay for in headsets and the cheap ones that cover the pilot shop shelves are just that ... cheap.
The Bose X is perfectly usable with no power which is good enough IMHO.
There are David Clarke headsets which are as good as the Bose for attenuation but they do it with heavy clamp pressure, which does your head in after 1-2 hrs. The Bose does the same with far less pressure and is OK to wear for 6+ hrs.
The downside of the Bose is that it is not so good for being kicked around and sat on etc. For that kind of usage you want to buy a dirt cheap headset. For yourself, get the best.