In order to give a feel that the little Galaxy S4 has something unique, Samsung is working on a new SoC in the Exynos 5 series which will be seen in the GS4 Mini.
The new SoC, the Exynos 5210, follows the existing 5250 Dual and the 5410 Octa processors. As per the naming conventions of the Exynos series, the generation is represented in the first digit followed by the number of core in the second. Hence the Exynos 5210 would belong to the Exynos 5 series and will have dual core configuration.
Our best guess with regards to the cores is the plain Dual-Core Cortex-A15 SoC. But the possibility of using a quad core structure with ARM’s big.LITTLE technology. Even though it would have four Cortex-A15s and four Cortex-A7s, just one group of four would work at a time.
Considering the rumours of the Samsung Galaxy S4 Mini having a 1.6 GHz processor, it is quite likely it is the Cortex-A15s powering it.