From what I've seen, the North American version should be better if anything for most users. The Exynos 4412 excels at gaming and applications with more than 2 threads. With just 1gb of RAM, the 4 cores aren't likely to provide much of an advantage in mulittasking performance. Especially considering most applications don't actually run simultaneously, but are suspended in the background until you switch back to them. In that case, the S4 versions should excel, due to the extra RAM to keep the applications in, instead of having to write them to the paging file. The S4 cores are also individually more powerful than the Exynos 4412 ones, and there are precious few Android apps yet designed to take advantage of more than 2 cores, and most just run on one core.
So, for everyday use, I would expect the more powerful, higher clocked cores to be a greater advantage than having twice the number of less powerful cores. And with double the RAM, it can keep more things active, making it better suited to multitasking, and pre-caching things in the background for a smooth experience from using the launcher and opening apps. The only real advantage I see to the 4412 is in gaming, due to the more powerful GPU (Mali 400MP > Adreno 225 from what I hear), and of course here the extra cores will come into play. But with all the radio support built directly into the SoC, 28nm vs 32nm, only half the cores for a more efficient sharing of TDP, and the ability to individual clock and enable/disable each core, I would expect the S4 to have the advantage in power efficiency as well. It's just like when quad-core x86's started appearing a few years back, but dual-cores still offered better overall performance and better efficiency for quite some time. I would rather have a dual-core cpu with more powerful cores than four cores that aren't as powerful. I would expect the same to hold true in the mobile space, especially here where TDP is at such a premium.
Before the SGS3 was announced, I was hoping it would get the Exynos 5250 (A15 dual-core, Mali T604) and would have native LTE support. Once I learned this wasn't the case, I'm honestly happier getting the S4 version anyway. Despite what benchmarks and hardware-intensive games may show, I would expect most of us to find the S4 version to be superior in day to day use.