The 5820K would have an advantage in the few games that can use many cores such as BF4, but the 4790K is already so fast that I doubt the difference could be noticeable.
If you're doing some modest multitasking, then the 5820K may be noticeably better, but even then I doubt it's worth worth spending around $700 on a new CPU, mobo, and RAM for that unless you specifically notice slow-downs with your current CPU. Basically, if it ain't broke, don't fix it.
Besides, the 5820K only really shines when overclocked for gaming since its stock frequency is a little low compared to the cheaper 4790K and similarly priced 6700K.