Why is the i7 7700k considered the best CPU

If your gaming it is, if you're not it's absolutely not. What are you wanting to do with your PC?

What games are we talking about here? Budget for the whole pc? Do you do any video editing?

Every game would be playable on a AMD R7 same for Intel i7. Now Intel has a slight lead in FPS in games. At the moment an i7 is a little faster solution at 1080P, when you jump to 4K the difference is fairly mute and 1440P you basically split the difference with an AMD solution. Traditionally in gaming single core performance has been key though there are some indications that may change soon with DX12. This is why the i7 7700K gets so much attention for gamers. Some newer games like BF1, Watch Dogs 2 and Ghost Recon Wildlands will take every core/thread you throw its way. The current gen Xbox/PS systems both have 8 cores and so devs are getting more savy at using multi-threaded CPUs. Point being there is a long game in choosing your new CPU for gaming. At the moment the i7 is dominant in gaming but the AMD Ryzen line is still very good in gaming. They are even better in productivity where more cores and threads are well utilized. Then there is the fact AMD is cheaper. Saving you money or allowing you to put more somewhere else in your build (say a nice m.2 drive?). Don't get me wrong I am not banging for AMD. Though I am admittedly fond of their Ryzen line for no other reason then it is getting Intel back in the game. They have been on cruise control barely upping their IPC over the last 7 generations. At 4K for example I have very little reason to upgrade my old i7 3930K @4.2ghz for the gaming aspect of my use because I'll only net another 5-6% in frame rate. Now if I were at 1080P it be more like 20% but that only be relevant if I gamed on a 120-144hz monitor where I could squeeze those extra frames out. On a UHDTV 4K at 60hz...it is a non-issue. My CPU uses two GTX 1080s with little to no bottle-necking. So My question to you is what resolution do you game at? What kind of frame rate do you find acceptable? If your making your CPU purchase souly on game performance then Intel i7 is the way to go but it sounds like you might not be. If that where true I might well consider an AMD R7 1700-1800X. You'll get more bang for your buck, especially if your gaming at 1440P (2K)-2160P (4K).

Do you have an unlimited budget for this upgrade? Have you purchased the 1080ti already or is it just on your radar?

If this was me I would go AMD. You plan on going to 4K gaming and want the most cores for the dollar then I would go with the AMD R7 1700 (if you plan to overclock) or the 1800X if you don't plan on OC or want absolute best OC (4.1ghz vz 3.9ghz on the 1700 approx, there is still a silicon lottery in effect). You could save some money and have a fairly future proof CPU that can stream your games/ watch youtube while you play them at the same time without your frame rate taking hit/stuttering, something a little harder on a 4C/8T CPU. Spend that extra money on a g-sync panel or m.2 drive like the samsung 960 evo. Heck you could even get an AMD R5 1600X with 6C/12T and still have a couple more cores/threads compared to the 7700K and save even more money in the process. Honestly the R5 1600X is the sweet spot in AMD's line up for gaming IMHO. Their 8C/16T parts just give you a little more future proofing and extra CPU horse power in multi-threaded apps. So whether you go with 8C/16T or 6C/12T, both solutions will excel at gaming while browsing/watching/streaming your gameplay video or just gaming alone. Again the i7 is the best gaming CPU right now but I think in the future the extra cores/threads AMD will offer you will be far more beneficial. Not to mention when your multi-tasking...ie playing a game while watching video (say a walkthrough)/game streaming or doing more then one task at the same time...the AMD CPU will be far better for your PC experience then the Intel equivalent. Things will be more responsive/faster then a 4C/8T part would be in those situations. AMD just seems like a smart choice. It costs less, performs better (exception is gaming as you know, and then it is a small difference) and gives you more as a platform then Intels 7700K does. Now if you strictly want the best frame rate today (may or may not be true in a years time or more), money doesn't matter, and you don't plan on doing anything while your gaming (no streaming, surfing web, music, etc) then the i7 7700K is probably for you better. I hope that helps.