Prices are nearly the same, but the VE248H has a GTG response time of 2ms, while the VG242H only has 5ms. The VE248H is reported to have ghosting though, although people fix that with turning OD off/reducing trace free.
A quick search I did turned VG242H to be a scrapped project of a 3D 120Hz screen back from 2009.
It was a typo of in the body of the post. Title has the correct ID's for products.
I'm not a screen specialist, but both these screens are really good. It's going to be a personal preference of yours.
The 2ms one also says Grey to Grey in the specs, that means it has a higher response time than 2ms. I've heard from somewhere that screens can go up to 10ms in response time when they use this selling trick for their products. Though this is all hearsay, might not be true. Someone needs to clarify.
This doesn't mean that it's a bad screen, it is a pretty good screen with a contrast ratio of 10m:1. If you have a chance, go see these badboys on display at a retailer. If not, both of them would be good. I'd take VH242H over the other one just because of the response time, but 10m:1 would leave me in a shadow of doubt. (If the response time thing is wrong and 2ms is effective, taking that screen would be better.)
Someone with a broader knowledge should probably answer your questions though.