Stallion behaviour, can be anything which would not be normal or common in a mare or gelding.
Stallions will often push down or jump fences, to get to mares in heat.
Stallions can often be 'bitey'.
Stallions can often be loud.
Stallions can be harder to handle than a mare or gelding, by the average horse owner.
Stallions will often 'fence-run' when seeing mares in another pasture. This can make them lose weight rapidly and not be interested in eating.
Lots of other things, make stallions very difficult. ALL colts should be gelded after weaning, unless bred by a very knowledgeable breeder, who might want to run one on to see if he might mature as stallion quality. Few are!
Very few horse owners, should own a stallion. They can be dangerous and difficult. Colts kept whole, should have very careful and serious training, from early life. They can become difficult and dangerous, very quickly, upon sexual maturity.
No children should be allowed around stallions.
Anyone keeping a stallion, should have extremely solid, safe and high 'stallion' fencing. Many lead a lonely life and will try their best to escape.
Poor quality and grade stallions are much more likely to end up in slaughter houses, after the owner can no longer handle them. Very difficult to sell a stallion, unless of very good quality.