The Exynos 5 Octa chip, just like Tegra 4, is based on the powerful Cortex A15 CPU core, and it should easily beat Qualcomm's best CPU this year, and even Apple's own custom CPU core (Swift), which is not only weaker in performance architecturally, but should also be significantly underclocked compared to the Exynos 5 Octa's own Cortex A15 cores. This should help Samsung maintain performance leadership in CPU over Apple.
Unlike Tegra 4, Exynos 5 Octa should also be more energy efficient thanks to its use of big.Little set-up and the very efficient and tiny Cortex A7 cores. The Cortex A7 cores should be in use most of the time, which could prolong the battery life significantly for most users, while it can also be very fast for the things they need like instant web browsing and playing very advanced 3D games.
It will be interesting to see how the Exynos 5 Octa will do in the GPU performance area, though. While their PowerVR SGX543MP3, which is what the iPhone 5 has, but probably clocked twice as high, should have twice the performance of the iPhone 5, however we don't know yet what will be the performance of the next iPhone's GPU.
The next iPhone should have a PowerVR Series 6 GPU, which could very well "only" have 2x the performance of the iPhone 5, and then it would have roughly the same GPU performance of the Galaxy S4. But one advantage the next iPhone is support for OpenGL ES 3.0 graphics and OpenCL for GPU computing. This is the main reason why I really dislike the fact that Samsung went with an old PowerVR instead of a newer Mali GPU for 2013, and if they were really keen on going PowerVR, they should've at least gone with Series 6.
Samsung plans to launch the Galaxy S4 with Exynos 5 Octa in New York, at the heart of Apple's home market, and I believe this time they will be more aggressive than ever in marketing. Apple has kept climbing in market share in US because a lot of Americans are very fond of Apple, the company, and of their devices, too.
It's very hard for anyone else to beat them there. But if Samsung plays all of their cards right, and they use marketing that portrays Apple's devices as "old" and "boring" (not having an overhauled UI in iOS 7 would help here), then they could potentially give Apple quite a beating. But the execution needs to be flawless, because it would still be a very hard task.