It is said that with wide rims for the tyre width, the sidewall is more exposed to sharp rocks tearing it. Well, if you look at the tyre shape, it definitely is more exposed. I had 32mm internal rims with 2.35 tyres and liked it. But I went to Antur Stiniog and got a slit in the sidewall just by the tread. So make of that what you will, but probably don’t go too wide if you ride regularly in sharp rocks.
With a squarer profile you need less lean to dig the side knobs in, which you may or may not notice depending on how you corner. I definitely noticed improved turning in and cornering, thus illustrating my poor technique.
A flatter tread area can lead to higher rolling resistance, even if you leave pressures the same, according to some theories which kind of make sense.