Hard to say without seeing them in person but just from the newegg site...
I noticed the 246H is rated as brighter (300 vs. 250 cd/m2). 250 sounds kinda low to me. I know that backlit LED's are supposed to be bright so maybe that makes up for it but still, I might be concerned about those numbers.
The other thing is the stand on the 248H looks flimsy compared to the 246H. Over time, depending on how your setup is, I'd wonder if the stand would hold up with vibrations from walking around, bumping the desk etc. Would hate to have a screen tilting just after warranty.
If you plan on using a VESA mount, no worries then.
The cabinet color is glossy on one and not the other. I don't know if that would translate to the screen as well but again, depending on setup and light, a glossy screen isn't for everyone due to reflections getting in the way. A glossy cabinet would show more fingerprints but not sure why anyone would need to touch the bezel anyway.
Guess I'd look into the brightness thing, and adding the stand concerns would probably sway me towards the 246H. Return policy on screens at Newegg?
Have fun

and enjoy whichever you get.