The two games don't sound all that similar. It's not an MMO, for one thing. I also doubt there will be as much focus on the economy or large-scale corporations. I think EVE is great, I like reading about it occasionally, but I have zero interest in playing "Ayn Rand's Battle Spreadsheets"[0].
There was a bit of ship customising; there were the missions; there was a mini-game of "land in the space-station without a docking computer and without crashing".
Planets had names, and some description, but that was just dusted on top of the actual game. You couldn't visit the planet. You couldn't get out of your ship on the space station. The space stations were mostly the same.
So Elite was really just buy low, sell high, with dog fighting and 3 factions. (Lawful, criminal, neutral.)
I dunno, it sounds pretty much like an early single player version of EVE.
There's no doubt that Elite is an ancestor of EVE and many other games. But clearly they're going to implement a superset of the features the original had, and I don't get the impression that the end result will be very similar to EVE. That said, an early single player version of EVE wouldn't be very similar to EVE, either; I get the impression that EVE is almost purely about player relations and the metagame.
On an unrelated note, you could land on planets in Elite 2. That totally blew my mind back then. Sort of like a real time lo-fi version of Powers of Ten[0] running on your computer.
[0] http://news.ycombinator.com/item?id=4625338