The advantage's of a taller tyre are as lay80n says
the larger the wheel the smaller the obsticle,
another one is that because your tyre diameter is larger the tyre lasts longer.
you also asked about width, and that is another can of worms
the wider the tyre the less pressure it puts on the ground, this is both bad and good,
let me explain,
a carton of milk holds a litre of milk and weighs about 1 kilo, if you wanted to hold a door open with one, you would stand it vertical, as its footprint when vertical is 3 times smaller than it would be laying down, it still wieghs 1 kilo no matter how you place it,
but when vertical it applys 3 times more PSI of downforce and is less likely of slipping,
this is an example of maximising downforce.
lets take that same milk carton and place it verticlly on some shag pile carpet (like the stuff Guy has in his bedroom
)
and place another one laying down beside it, after 10 mins if we remove both, we will find that the vetically positioned one has left a deep impression in the pile of the carpet and the one laying down has hardly left a mark,
this is an example of maximising floatation.
to put it in an automotive perspective (I know some of you petrolheads have brains the size of peanuts
)
if a car weighs 1000 Kilo's and is perfectly balanced (front to back/left to right)
each axle is supporting 500Kg and each wheel is supporting 250Kg, the front axle has 6" wide tyres and the rear has 12" wide tyres both are the same height, (anyone see were I am heading with this
)
lets go for a drive in our full time 4x4,
first we go up a hill that is covered in shail and loose small rock, the front axle, with twice as much PSI of downforce applys twice the pressure and grips the surface where as the rear is spinning all over the shop!
wow that was fun! lets go for a drive down the beach, we find the front wheels sink in the soft sand because of that heigher PSI and the rear axle just floats over the top
lets go for a drive in the snow (this is a tricky one)
we find that the wide tyres use more power to push through the snow than the 6" ones, but the wider tyre has the benifit of not sinking in the snow as deep and indeed on occasion floating over the top
now I know StevieG will pipe in with a comment about the angle of the hill will place more weight on the rear axle or that the car in the sand had a Hyclone or something but you get what I am trying to say here.
Peter.