The price difference between the i7-3770 and the i7-3770K is about $20 - $30 if you shop around.
There is a performance difference even at stock speeds. The K is 3.5GHz per core; the plain 3770 is 3.4GHz per core.
Check the CPU benchmark here: http://www.cpubenchmark.net/cpu_lookup.php?cpu=Intel+Core+i7-3770K+%40+3.50GHz&id=2
and price/performance here: http://www.cpubenchmark.net/cpu.php?cpu=Intel+Core+i7-3770K+%40+3.50GHz&id=2
Even though the plain 3770 is rated slightly higher in price/performance ratio and the 3770K appears to have a relatively small performance advantage, look at it this way: 3 - 4 years from now, when the new Haswell / Broadwell platform is out and we are running Cubase 9 and goodness knows what plugins and VSTi's that take advantage of the latest computer performance available, wouldn't it be nice to be able to overclock, or at least have that extra bit of juice from your CPU?
Anyway, that benchmark used a combination of tests, some that don't have much relevance for DAW work. I have seen DAW benchmarks (at stock speeds) that indicate even higher performance gains with the 3770K over the 3770. Apparently there is more under the hood than the extra 400MHz gained. And CPU speed is the 1st factor for lower latencies (generally; provided there are no other bottlenecks, like slow RAM or a bad mobo layout; 3 years ago, I replaced my BGF 680i mobo with an Asus 680i mobo and immediately noticed a difference, without reloading the OS).
I've seen a lot of Asus P8Z77 mobo + 3770K DAW builds listed; I don't recall seeing any 3770 builds.
People on a budget usually go with the i5-3570K ($80 - $100 less, 4 core, no Hyperthreading).
Another point: the K is unlocked for overclocking. Intel would not certify a CPU for overclocking that can't take it (okay, a debatable point). Chances are the K will be more robust and last longer if you run it cool at stock speeds.
If you are on a super tight budget, I am sure the 3770 (or i5-3570K) will be fine. I just like to 'future-proof' my build as far as possible.
Also, if you are considering AMD, you should know that they have stopped competing with Intel for high performance, so don't expect a good CPU upgrade to become available on that platform. Plus, a comparable AMD processor draws 125 watts compared to the 3770K's 77 watts. More watts = more heat = noisier (or more expensive) cooling + higher electric bills and possibly shorter lifespan.
I also like Asus; it is up to the feature set you need, like # of PCIe/PCI slots (bandwidth dictates a limited combination of each), LAN, Wi-Fi, etc. The Intel LAN on the V, V-Pro & higher is supposed to be better & more efficient than the cheaper chips used on the LX, LE & LK. Also, the V-Pro & up have more PCIe, Sata and USB lanes and/or ports and better controller chips. YGWYPF.
The V, V-Pro & Deluxe have progressively more power phases and digital power control, if that means anything.
And you can take a chance on the V-Pro Thunderbolt for a few more bucks than the V-Pro, but you lose the Display Port & the 2 USB 2.0 ports on the back (but there are 5 2x internal connectors for up to 10 USB 2 ports, if you have a place to mount the expansion rails). There is also sharing w/ the TH, one of the USB 3 ports and one of the Sata ports. I think you can turn off TH until you need it (in a couple years...) to free up that bandwidth. I'll let you know how the Asus V-Pro/TH works in a few weeks, if all goes well.
Hope this helps.