I can compare them because I am intimately familiar with the both core processors.
The S4 may only have 2 cores, but they are about 40% more power efficient due to being manufactured with a 28 nm process. Further, the cores are basically A15 class rather than the A9 cores found in the Tegra 3 quad. Much more horsepower per core. So comparing quad vs dual cores without looking at the whole picture is like comparing a V8 engine with a V6 without considering displacement, horsepower, torque and fuel delivery.
For day to day tasks, note that the S4 is using separate cores for video and media as well as the user interface than the GPU. I believe that quite a bit of that info is in the linked data I provided.
The Tegra 3 I would expect to perform a bit better on heavy duty games.
Right now, it appears that HTC is still fine tuning the quad core kernel.
Otherwise, were I to give you a day to use each one for most anything else you can imagine and then ask you which was the quad, you'd likely only have a 50/50 chance of guessing correctly which was which.
I would submit that a One X is a One X and the blogosphere is virally selling people on meaningless synthetic benchmarks and buzzwords.
For each sort of thing where the international will excel, you'll find another where the ATT model does better. In the end, it's a draw.