Both GPU companies are really good right now. You pay a premium for Nvidia GPUs and they have their stuff in a closed ecosystem (Shadowplay, Gsync, etc). I currently have a 970 and love Shadowplay but I love what AMD is doing with Freesync, and I'm pretty sure they have their own version of Shadowplay as well. You've only been fooled by Nvidia's marketing is all. Nivida and AMD are both good.
Go for whatever offers you the best features and performance for the price it is sold. Do games you play/tasks you do take advantage of CUDA or PhysX? Do you have to have Shadowplay? Do you have a G-sync/Freesync monitor or are you planning to get one? etc. One thing to note is that the AMD 300-series GPUs support DX12 which is something up-and coming thanks to Windows 10. Nvidia's 900-series currently do not support DX12.
Multitasking is more dependent on the CPU, and an i7 is more than enough for that. If you're in the 300-350 price range, get an AMD R9 390 Sapphire Nitro. If you're in the 600+ range, get a 980Ti.
AMD is a good GPU company too. Nvidia also has nothing in the $400 range, there's a huge gap between 970 at $350 and 980 at $550 (not worth it, only 10-15% better than 970). If you really want it to last a long time with *no* upgrades, you'll need to spend $2K and go for a 5820K and a 980Ti. If you can't afford that, a 390X will be good for 3-4 years, and is much easier to replace than CPU+board so you should go for 5820K+390X. Yes they do. They don't have native hardware support for asynchronous compute, which is done by driver instead with performance almost as good as AMD's. They also support a few features AMD does not. But neither Nvidia nor AMD have *full* DX12 support right now.
Support came the same day Win10 came out. Nvidia does that with every "major" software release. An "optimal" driver for the latest game on (or the day after) release day.
I gave you a very good parts list for under 2k. That will last you a long time. The 6700k will last for years. Some people still run i7 920s today which are really old intel 4-core processors. Yes, a 5820k might last longer, but Skylake is a newer platform so I think it will be more future proof.
5820K is way more future proof, and will last longer. As I said before, HT is worthless for gaming, you want Skylake, save $100 and go for an i5, will last just as long as a 4/8 i7. Also, never ever buy a Windows OEM license. Swap a part and it becomes useless.
https://pcpartpicker.com/user/bluescreen1985/saved/ZvknTW 5820K, 980Ti. You can replace the HDD for a higher capacity one and stay within $2K. Bonus points for looking really awesome with all matching colours. Edit: http://pcpartpicker.com/p/4mZpcf Exactly $2K with Windows 10 Pro.