I know the rule for regular vehicles (so I would assume it's true for large vehicles as well) is that the exhaust must exit BEHIND the passenger area (to reduce the amount getting sucked into the passenger compartment). So it's OK for trucks to have it dump out before the bed, but buses must have exhaust that exits at the back of the vehicle.

After that it's primarily what's easiest to route the pipe. It's pretty easy to route it straight back down the underside of the vehicle. Front-engine school buses are basically just regular trucks/vans scaled up in size.

I strongly suspect that city buses are subject to more regulations regarding emissions, noise, etc. than school buses. It is amazing how many special rules there are for different types of vehicle (logging trucks for example get to ignore almost every single safety requirement for their trailers).

I also suspect school buses are quite a bit cheaper than city buses. Every single rural county has to have at least a few school buses, but normally only fairly decent-sized cities have city buses. So school buses are probably designed on the easiest/cheapest rule.