well Galaxy S4 use two processor Some of them use Snapdragon 600 processor which is a quad core processor that is used in the devices with the code of GT-I9505 , the other one is indeed use a octa core Exynos 5410 . well this processor is interesting because if you look at the core configuration it's consisted of Quad-core 1.6 GHz Cortex-A15 & quad-core 1.2 GHz Cortex-A7 what is important is at a time only 4 core of the same family is active if the phone need high calculation power Quad-core 1.6 GHz Cortex-A15 will be active otherwise if the phone is Idle quad-core 1.2 GHz Cortex-A7 which is a weaker core but far more power efficient are active so the power of the phone has nothing to do with being 8 core but it's due to using a newer architecture which is Cortex A15 compared to Cortex A9 in Tegra 3 and Exynos 4412 and Apple A6.
now about the power of tegra 3 and Exynos 4412 . let be objective the speed of the processor can't be a good comparison (if it was so then The AMD processor would have ate Intel ones for breakfast but the truth is something else) the fact is that Exynos 4412 at 1.6ghz which is used in Note 2 is faster than Tegra 3 AP37 which is used at HTC 1X+ but Exynos 4412 at 1.4Ghz that is used in Galaxy S3 is slower than that processor but faster than original Tegra 3 used in HTC 1X .
these are some benchmark of those processors
HTC One X+ review: The complete package - GSMArena.com
here you see the comparison of the speaker of those phones
HTC One X+ review: The complete package - GSMArena.com
by the way Your link show Galaxy S4 GT-9505 Faster than Galaxy S4 GT-9500 which is wrong
and about that oily patch , to be frank never seen one in real , that must have been some random damaged screen
Sonny when partnered with Ericson made bunch of lousy phones but after separated its way they are actually making some decent phones