For gaming the 6600k without a doubt.
But what about the 4 extra cores if i also want to do some multitasking.
Compared with the FX, the i5 can do four things twice as fast, or 8 (or more) things at the same speed as the FX, because each core is so much more powerful.
To put it in perspective, the FX's cores are each about as fast per MHz as Intel's ~2006 Core2Duo CPUs, and in both single- and multi-tasking, are still completely outperformed by the first generation Core i7 which was released in 2008.
I'm not saying the FX CPUs might not do what you want, but so might an Intel PC from 2008. That doesn't make the FX a better choice than a modern i5.