I'm giving you basics, so you put it together however you need to decode. @Wrangeld is almost right on everything, Ill add few more clarity points.
Any increase in tire size: width or height will help in increasing sand flotation to have bigger footprint, however length increase is tad better to give flotation + ground clearance (which is prime requisite in off-road). Width is better when you need to increase the center of gravity by widening your stance.
Tire weight is the prime factor, that many people don't research, understand and factor as not many manufacturer like to share this data. Having bigger size tire, which is lighter than smaller tire is better for off-road long hill climb and better for fuel mileage because you have less weight on per axle to rotate.
Tread size and pattern cause major difference in off-road and on-road (comfort and mileage) than tire size or weight alone.
In your friend case 265 -275 is mere 1 cm width, that is TOTALLY NEGLIGIBLE for comfort, mileage, noise, offroad etc. unless you share more data of which tire brand, tread and size he used like 265/65/17.
The more detailed information you share with your precise requirement, the better and productive advice you will get.