Actually no. When given the choice between my International One X (Tegra 3) and an AT&T One X (long story, insurance replaced the international version with an AT&T version because they didn't pay attention), I chose the AT&T version due to the S4 which is newer architecture and is very comparable to the Tegra 3, even beating it in a number of benchmarks. Plus, the battery life is far better. (And in the case of the One X, the Tegra didn't have LTE, not a consideration for you though).
That said, I do put the Exynos 4412 a little above the Tegra 3, so I think the difference is a little larger between the two, but you're basically arguing about which of the elites is better... well, not so much elites at this point. The S4, Tegra 3, and Exynos 4412 are all fast enough to run the Android OS perfectly smooth and with no noticeable difference. If you are a gamer, the Exynos has the Mali 400 GPU which is better, but as far as processing power there isn't a noticeable difference. The bigger difference you saw between the devices was that the Note II was on JB and the SGS III was on ICS.
Yeah but no only that but for what I do, the screen on the Note 2 is much better for me to work with. I have to look at a lot of diagrams and that screen is just sweet for that. I also conenct remotely to PCs so the screen helps there as well. The S3 is a fine phone, don't get me wrong, but I just prefer the screen size of the Note 2. I am quite sure that S3 will perform great on JB. Haven't seen any official test reviews on it yet but I am curious as to how that S3 performs now with JB.
As far as gaming is concerned, I'm old school so I don't play games on my phone, that what the PS3 is for...LOL.