What processor is better and why?

AMD has pretty equal performance to its Intel counterpart, but it gets a lot hotter. On a desktop that's okay as long as you get an aftermarket heat sink, but for laptops I recommend sticking with Intel, because AMD laptops tend to overheat easily, which can damage a number of computer components (and even start fires if you accidentally leave it on a soft surface like a bed or sofa!).

If you're serious about gaming, I would look for something with a Core i7 quad-core processor.

Better is AMD A6-4400M:
1. The microprocessor performs 190% better in graphics programs and games.
2. This CPU has AVX, F16C, FMA3 and XOP instructions enabled. Although these extensions are not extensively used by applications yet, their support should improve in future programs.
3. The microprocessor has FMA4 instruction set extension enabled. Only AMD microprocessors offer this technology, thus not many software vendors may support it in the future.
4. Somewhat higher performance in all application types,
Performs significantly faster in graphics applications,
Features AVX / F16C / FMA3 / XOP instructions
All the best!

The Core i5 is slightly better than the A6 in CPU performance, CPUBoss rates it at 6.6 vs. 6.1, so it's a negligible performance difference.

Intel Core i5 560M vs AMD A6 4400M
http://cpuboss.com/cpus/Intel-Core-i5-560M-vs-AMD-A6-4400M

The A6 however, has much better GPU performance than the i5. It's embedded GPU is called the AMD Radeon HD 7520G, which is DirectX 11 compatible so it will theoretically play all modern games, though that's dependent on actual performance of the part.

AMD Radeon HD 7520G - NotebookCheck.net Tech
http://www.notebookcheck.net/...728.0.html