IMO, the Elantra has little to fear from the Accent, different types of vehicles. The Elantra is bigger/heavier and yet gets very similar mpg. And, the Elantra seems to me at least, a tad more sporty, while the Accent, especially the hatch, a bit more utility. I'd compare it to Civic/Fit and Focus/Fiesta.
And then there's the much discussed Bitog concern about possible DI valve deposits with the Accent. That said, I doubt for the average non Bitog buyer that will be a consideration.
I think Hyundai has a winner in both major redesigns with the Elantra and the Accent. I see no reason, especially with gas prices, why they both can't flourish.