I'd go with the Intel i5. As you mentioned indeed the i5 is older, but the newer AMD A6-6310 doesn't provide any benefits as opposed to being released later. The i5 will provide you better performance regardless of the core count.
The Intel i5 Mobile has 2 cores but also Hyper Threading (HT), hence the OS will function as if it's a quad-core processor; the HT doubles the thread count. Naturally 1 core is 1 thread, 2 cores are 2 threads, however with Hyper Threading, 2 cores become 4 threads and the OS will treat the 4 threads as a quad-core CPU (if that makes any sense
).
The AMD offering however is genuinely a quad-core processor, however it's per core performance (single core performance) is not up to par with Intel's offering; hence the i5 will serve you better. For daily home/office tasks either processor is adequate, however I'd still go with Intel due to it's increased performance over AMD in this scenario.
All the best.