I am looking at buying a 2008 Elantra SE but want to know what the difference is between these two, besides the horsepower and torque output:

hp @ rpm ULEV = 138 @ 6000
hp @ rpm PZEV = 132 @ 6000

Torque @ rpm ULEV = 136 @ 4600
Torque @ rpm PZEV = 133 @ 4600

What is different on the cars themselves that makes one a ULEV and another a PZEV?

Is it just a different catalytic converter on them?

Will this affect how it drives in a high altitude state or while going over mountains?

I seems to me in order for each car to reach the same speed, the PZEV will burn more gas and therefore, maybe pollute more than an ULEV?

I think you will find the only difference to be in the computer controled timing and air/fuel ratio.
The PZEV is adjusted to put out slightly less environmentally hazardous flourocarbons.Some of which are too slight to be measured.Hence the name partial zero emissions vehicle,versus ultra low emissions vehicle which still register all the common types of flourocarbons although in very low amounts.
Personally I would get the one with the most torque and horsepower.One for the reason you stated above ,two for a less anemic feel.