tl;dr: Fatter tires are slower, I feel it's not worth it.
I ran both the 2.0's and 2.35's around their max pressure. The fat ones seem maybe around 1.5 - 2X wider and the bike I used them on has mtb type inch wide rims, so I had issues adjusting the V brakes. I was able to fit V's and freddy fenders, but cantis would have been better.
They're very definitely better at preventing diversion, like going up a sidewalk lip at a sharp angle, or the cracks in the street that are in line with the direction of travel. Also noticeably better at going down stairs, rescuing the bike from failed pops (mostly jumping sidewalks).
First impression was that they were heavy. The 2.0's are already quite heavy tires, kinda like what comes on a department store grade mtb, but instead of being crudeness it's the built in anti-flat thing. I still have 0 flats to report with no tire liner or anything, btw. But anyways the 2.35's made the wheels feel a little heavier, not good for the start/slowdown/speedup/stop type riding I do to get around.
Then, they don't roll as foreverly as the 2.0's seem to. Where at low speeds the 2.0's felt almost like road bike tires, the 2.35's felt more like a worn 1.9 knobby at max pressure.
Once at speed the 2.0's show their width through aero, and the 2.35's show it a lot more.
2.35's allow harder/more confident cornering then the 2.0's, especially on sand. But in most cases the bike feels more nimble with the 2.0's. 2.35's felt much better rolling over grass, less bumpy. They were also much more capable up 45 degree slope of wet grass, however they still suck at that.
With the 2.0's I can be crouched back over the seat with rear wheel locking up a bit and slightly skipping from hard braking up front. Braking any harder would cause the rear to lift up, so more traction is moot. On sand/grass etc I'd imagine the 2.35's would fare better, but then again I'm nearly always on pavement.