I operate a Bo out of unimproved strips sometimes in NM, and TX. Of course grass is no problem. The Bonanza will also take the 8" Cleveland wheel and 6.50x8 tire on the main gear. It's the same size as the Baron tire, and does fine with modest gravel strips. It's not going to be suitable for a river gravel bar, but in comparison to a 182, it'll do fine.
As with everything, there's a point of diminishing returns. Picking up stones, and gravel, and spraying it on the tail of the plane just isn't something most Bo owners are willing to put up with for the most part.
That said, the amount of time you are spending getting in and out of the rough strips is a function of how you want to handle ground work. Maybe the 182 will be better for the rough stuff up in Idaho, and MT. It is what it is.
In the air, there is just no comparison. The Bo has it all over the 182. Of course, the Bo is rated to Utility category, right up to gross weight, unlike the 182 which is sadly, only rated to normal category standards. Speed/efficiency is better, but you only get one door. So, if you need two doors, well - you'll have to settle for the Cessna.
Now, ask yourself how often you are going to operate at full gross, out of rough strips? If you are needing that big load, and gravel capability, get the 182. Just cuz it drives like a Chevy truck, and uses more gas than a Lamborghini is no reason to avoid them. There's lots of Cessna folks out there that are perfectly happy with their 182. Lots of Chevy owners out there too.