Traction relies on contact pressure.
The wider the tyre the smaller and wider the tyre footprint on the ground and less contact pressure.
Taller tyres have a larger and longer footprint and therefore greater contact pressure.
Muddy and rocky conditions you need as much contact pressure as you can get to gain traction to keep momentum up.
The only time this works against the vehicle is on soft sand. There you want a wider tyre with very little tread so that the tyre "floats" on the soft sand. The more tread the more the tyres will dig into the sand and bog the vehicle.
If you are doing majority of tarmac driving A/T's is probably advisable over M/T's.
If you have the room under the wheel arches use traction chains to aid offroading in muddy and slippery conditions. You'll be surprised just how much further you can take it.
Vitara's without a lift can't go too much bigger wheel size wise without rubbing.
They tend to get bellied pretty easily without bigger wheels. I had to massage the guards as well as adding a lift on the Vitaras I owned.
Edit: Forgot to say Vitara's need to have a wider track as well to help them falling into ruts from other trucks, so choosing a wider offset wheel will help that issue. But then the guards may need a bit of a chop, and add on flares at the very least.
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