I've driven an sr5 before, it was pretty sweet I gotta say, and I think stock for stock I'd take the corolla on the track... HOWEVER... The s12 sits wider, it squats more... Modded vs. modded, the s12 is easily the better choice. The first thing the s12 needs is suspension suspension suspension. It's heavier weight makes it more difficult to change momentum (because there's more momentum), however, the wider stance is going to give you more stability in the corners in the long run.
The SE may be a bit nose-heavy, but that's not right away a bad thing. Once you start adding power, a little nose weight is what you need. You should be starting your throttle on as you enter the apex of the corner, that puts the weight on the rear tires. A balanced car like the corolla is going to start to understeer more at that point and requires feathering the throttle off and on in order to keep the car balanced, while the slight addition of nose weight in the SE-s12 keeps the steering naturally neutral as you throttle on.
The s12 is made to be aggressively driven, with full coilovers it requires harsh treatment but that's part of the fun of it. A modified s12 platform literally begs you to assault late-apexes with early throttle-ons. The modified gt-5 corolla, while balanced, demands a more laid-back stance behind the wheel. What fun is that? I'll admit, that in a pendulum-slide situation, the corolla will be easier to handle for beginners, but once you learn to use the more aggressive s12 setup, you'll be happy you did.