Potential CPU/MOBO upgrade to Intel 6700k

I am currently running an AMD 8320 system that is OCd to 4.4 Ghz, 12 Gb 1600 RAM, a GTX 970 and has numerous ssds. I've had the system for approx. 3 years and have that itch to upgrade now that Skylake has arrived and settled for a few months. The system is used mainly for gaming and streaming to my Steam Link in our living room. I run most games with DSR up to 2x and can still maintain 60 FPS. I was hoping i could get some input on the cost effectiveness of upgrading to a 6700k CPU, with 16 Gb 3000 DDR4 system. Would I miss out on the extra threads if I were to just get an i5 6600k or am I just pissing money away and should wait until later this year? Any thoughts are welcome, especially user feedback from individuals that have used both CPUs.

is the the best cpu?

in terms of gaming + streaming, i would definitely recommend to skip on the i5 but directly go with the i7.
The i7 has more threads and will get better performance wenn streaming.
For the rest it highly depends on the games you play and how you play them mainaly.
cpu demending games or cpu demending gaming scenario´s like heavy multiplayer you should definitely see some improvements with an i7 over your current FX especialy at 1080p.
But there are ofc also GPU demending games like Tombraider for example, in which the performance increase will be realy minimal.

I play a wide variety games including the new Tomb Raider game, Skyrim with mods, League of Legends, Deus Ex and occasionally BF4. I know for a fact that BF4 pulls all my CPU can give it or at least all the cores are active. My main concern would be losing gaming power when streaming to the steam link, as more thread should be beneficial in that aspect correct? Similar to streaming to Twitch?

With the i7 you should be totaly fine.
You can stream with an i5, using quicksync but its not that great.

If you realy need some extra cores and threads?
maybe you could also concider a 5820K on X99 instead then, and overclock that
Then you have 6 cores 12 threads.
But basicly a 6700K should be totaly fine for streaming + gaming aswell.

Should get a Xeon 1231v3 instead, way better for the money

Or if you're in the US get the 5820K. More cores. And cheaper. Platform is slightly more money but it will be Les or about the same. Possibly slightly more in totally.

You'll get more cores though and quad channel RAM. OC it and it will be faster in games.