I have a D800e (just got it) and a lot of Nikon equipment, including a D3 and the 3 f2.8 zooms and a half-dozen primes, and various bits and pieces. I also have a very complete Panasonic set, including 2 G1Xs and a GH2. This is going to sound odd, but when I'm doing photography for photography's sake, I now always use the Pannys. (At this moment, I am sitting in a hotel room in Jerusalem, killing time before I get on a flight back to NY. I have with me the 2 D1Xs and four lenses, and no Nikon equipment.)
The Nikons I use because I'm a painter, and though I spend a lot of time looking at things, I find that photographs can often teach me more about what I'm looking at than the eye can, especially with landscapes. You can do all sorts of on-the-spot sketches, but when you're back at the studio, you almost always find that there is something that you don't understand. A photograph, especially one that is capable of massive enlargement, will usually explain the problem. That's where the D800e will prove invaluable. The thing is, you often do not know where the problem is going to be, so you take overall photos and then go deep into them to solve your problem.
So my answer to the OP is, it all depends...for the kinds of *photographic* things I do, the Panasonics are good enough now, and they will get better. I will be quite disappointed if the next generation of Pannys (the DH3 and the D2X) don't match or better the OMD. If I were to print larger than I do, or cropped more severely, or shot a lot in very low light, then they wouldn't be good enough, and it might be a couple of generations before they do get good enough.
If you can afford to, I'd keep both systems. They are really quite different, and both are excellent for what they do.
As to the technical quality...the D800e is nearly as good in low light as the D3, and some will say better. Since the pixel (or sensel) size is roughly the same as in the Panny sensors, that means the Panny sensors should eventually be able to perform as well as the D800e. Of course, they will still be smaller sensors, with fewer pixels, so you will not be able to print as large with the same level of fidelity...but you should still be able to make very substantial prints with resolution as good as the D800e's...eventually. How long? Who knows? By 2015? Maybe.