The difference is that it gives the time to 3 decimal places. Which means that if you have two people at around the same time, while in the normal Super Pi they would both have 48 seconds, in Super Pi Mod you would be able to tell which one was faster. Bascially, it means its easier to differentiate. It's also more accurate.
Some people may say that it should take advantage of everything. But the idea is to try and have the CPU at 100% load, not both CPUs. It was also written before dual cores were released. About the HyperThreading, though, and a bit more about Dual Cores now
If you want to test both cores, you can download it twice, install it twice on two different directories, and run it twice, one core on each .exe. That then stress tests your PC. It's the same with nearly every other stress tester though, even Prime 95 has to be run twice.
There is one other main problem with the normal Super Pi. The scores are amazingly easy to change. They are listed in a text file, so all you have to do is change the value. It would be pretty easy to spot if someone had given themselves 0.99 seconds, but what if someone had just knocked 3 seconds off their time? That would give them probably a higher place, which is cheating. On Super Pi, the results are encrypted inside the program itself, if you change them then you kill the program, so you can't cheat