From all the research I've done the only major advantage the i7 3770k will have is hyper threading, which games don't utilize and from everything I've read likely won't in the near future (10 years). They are both ivy bridge processors and thus will use the same type of components. So I see no reason that any GPU upgrade would ever work for one and not the other.
It varies depending on what you're doing. Even then however - you'll barely notice the difference unless you benchmarked. Like stated above, the only 'major' difference is HT, which is only of use in 'multi-core' applications (e.g. you'd notice better vm performance, faster rendering?, etc)
To save my breath - just get the 3570K and the D14. It's simply not worth the extra cash to get the 3770K over the 3570K.