As a general rule, Edwards are the 'factory made' guitars (I'm not sure but maybe outsourced, like Ibanez being made by Fujigen?) and ESP are the 'handmade' (presumably by ESPs own staff). But both are made in japan and are great quality. I think if you get the ESP you'll have better inlays/binding/fret work etc but Edwards are pretty decent.
The other thng to think of of course is resale value, the ESP will keep more value than the Edwards.