Pros and cons of each chip:-
AMD Ryzen 1600X:-
3.6 GHz @ 6 Cores, 12 Threads, Turbo 4 GHz, 16MB Cache, 65W TDP
Pros:-
) A great alternative for better workflow than the I5.
) One of the best game and live streaming line up currently in the market.
) More cores - the 1600x has 2 more cores, 8 more threads and double the amount of cache the 7600k has.
) As all of the Zen processors are unlocked, so you can gain extra 100-200 MHz by overclocking through BIOS or the AMD Ryzen Master program. The lower TDP gives Ryzen even further room for overclocking.*
Cons:-
) Lower clockspeed means it's not going to be that great at gamnig.
) Less RAMs and cooling soltuins are compatible with the Ryzen family as of now, compared to Intel's Kaby Lake family.
) No integrated graphics in the chip.
Intel I5 7600K:-
3.8 GHz @ 4 Cores, 4 Threads, Turbo 4.2 GHz, 6MB Cache, 91W TDP
Pros:-
) Higher clock speed and turbo speed, making it better at gaming and some Adobe programs compared to Ryzen.
) Better compatibility accross the board, so cheaper RAM and Motherboard options are available.
) Has integrated graphics card.
) All K chips are unlocked and are overclockable.*
Cons:-
) Lower core count, so it falls back compared to Ryzen when it comes to productivity(video editing, 3D sculpturing etc)
) Not as great at live streaming as Ryzen is.
) Higher TDP.
Personally I'd recommend going for AMD Ryzen 1600X if you are in a budget while wanting to own a computer that is capable of doing somewhat heavy workload, like video editing or live streaming. Otherwise, if you game a lot without doing workloads or multitasking that often, then go for the 6600K, 6700K or even the 7600K - 6600K is a better value chip out of the three, but it is your choice.
I built my newest computer with a Ryzen 1700 chip as it offered a great bang for the buck, and it is a 8 cores 16 threads monster so it makes me capable of doing a bunch of things in Blender and video editing in After Effects and having them minimized while playing GTA V with no problem at all.
* = Make sure to have a better cooling solution, like water, as these chips can run hot.