The 4670K motherboard would give you a slightly *better* upgrade path, but both are essentially "dead" sockets at this point - with used i7's for either socket viable upgrades from either i5.
Gaming performance difference between a 3570K and a 4670K, when paired with the same GPU, should be near identical. Generational improvements are <10%, nearer 5% in most cases. The 3570K should also be a better overclocker, so should clock higher..... at which point it's the "better" chip.
I don't really see any point in that "upgrade".
BadAsAl :
You won't have to reinstall Windows but it is still not worth the trouble in my opinion, you are talking less than 10% improvement based on the scores on PassMark.
You really should though. If it were a Sandy to Ivy (both 1155) upgrade, then you'd be fine without.
To go from a 3570K (1155) to Haswell 4670K (1150) though, you're replacing the motherboard - and really should be reinstalling your OS.