Phenom II X4 965 vs i7-2600k

I have an odd and probably very easily answered question, but in case I'm wrong, I'd rather ask you quasi-professionals than potentially waste several hours for minimal gain.
I recently came to be the owner of a free i7-2600k computer. It was a work computer for a client that the company I work for does IT work for. About a week ago, the computer refused to turn on whatsoever, and after minimal troubleshooting, the company decided that it was not cost effective to spend any more time on it and just tossed it and used a new one (They had like 6 spares)
My company is fine with the technician (myself) collecting old parts from client's old computers as long as the client is properly taken care of and we have a decent amount of used 'backup' in stock. I noticed that the case said 'i7' on it, so I figured i'd just take the whole thing and look at the innards later to try to tell what's up.

I get home and open it and see immediately that it has 8Gbs of 1333 DDR3 ram. (2-4Gb sticks). Not back. I see the 500GB Western Digital Blue hard Drive. Not bad either. I take the heatsink/fan off and wipe the thermal paste off the CPU revealing the i7-2600K tag. Well, kick ass!
I applied a bit of Arctic Silver and reinstalled the fan. I figured I'd start at the top with trying to figure out why it wouldn't boot and installed an old PSU that I had left over from a previous salvage. The thing started right up! Huzzah!

So now, finally, my question: HOW MUCH better is an Intel i7-2600K than an AMD Phenom II X4 965? Sounds stupid, I know, but I'm serious.

My current build was done on a massive Black Friday sale budget, but it has served me amazingly for almost 4 years. The Phenom (4 cores, overclocked stable to 3.7), Xigmatek Gaia aftermarket heatsink, 8 GBs of 1600 DDR3 (2-4GB sticks), 256 GB SSD, 1 TB HDD, AMD HD Radeon 5770 GPU. This build has served very well and has played every game I've ever tried on default Ultra High settings. It boots up to ready in about 10 seconds and is actually very cool with the Xigmatek heatsink, even for a Phenom. Fastest computer I've ever used, honestly. I've never had any problems. (Actually, I am just recently with the GPU; artifacts and whatnot, but that's a different story.)

Would it be worth it to trade the Phenom and AMD motherboard out for the i7 and Intel motherboard?
I know that the i7 has hyperthreading capibilities, essentially making it an 8 core. It also has 2 more MB of L3 cache than the Phenom. It's default clock is the same, which is great.
I've also noticed that the Intel motherboard only has 2 ram slots, vs my current AMD motherboard having 4. If I stuck with the Phenom, I could take the extra RAM from the Intel board and add it to my AMD board. (I know, it's not typically recommended to use different RAM speeds with each other, but I've never noticed any issue in doing it before). I could then have 16GB vs my current 8GB.

Obviously there's the physical work; removing and moving, reinstalling the Xigmatek heatsink (I HATE HATE HATE the way Intel heatsinks mount; I've broken several). But then there's the driver issue of moving brand name processors and motherboards and everything. It'd almost be easier to do a clean Win7 install than fight with the potential issues that could arise. This, of course, takes time though.

The i7 will OBVIOUSLY be better than the Phenom. My question is, HOW MUCH better? Will it be noticable? Will it work any better in my gaming/ media (my primary use for this computer)? Will it be worth the time an effort spent working on it? Will it be THAT much more 'future proof'? Will my current Phenom with 16GB of RAM be comparable to the i7 with 8GB or RAM? Any thoughts would be great.

P.S. I love my job. Free stuff galore.