It would depend on what resolution you running, and how high you are running all the eye candy, and AA/AF.
Under most conditions, I would venture to say the 4870 is still a faster card.
Although I have not seen benchmarks from the 4800 series on this, it was proven on the 3800 and 8800 series that anything over 512 meg of memory on a single card was more of a marketing ploy than anything. In fact, in most benchmarks, 2 identical cards except 1 with 1 gig of memory and 1 with 512 meg of memory....the 512 meg version of the card 90% of the time was faster.
Running the 2 cards with 1 gig in Crossfire or SLI did show some improvement, as 2 cards together can run higher res, and higher settings all around and the extra memory did show it helped some, but not a significant amount over 2 -512meg cards.
It would be interesting to see if the new cards do indeed make better use of memory over 512 meg than the last series.