Nikon, as one of the last, has finally stepped into the bustling arena of battling compact cameras with big sensors, with Coolpix A. It has a large APS-C sensor, but no image-stabilization.
I would say the two most prominent features are:
1) A fixed, non-zoom lens, at 28mm equivalent, and F:2.8 (not so fast these days).
2) It's surprisingly compact, much smaller than the nearest competitors, I'd almost call it a true compact camera despite the large APS-C sensor. Lo:
So if you like all that, this may be just the thing for you.
For me, personally though, I think they made the same mistake as Leica did: go with too big a sensor, necessitating big compromises on the lens.
With the amazing sensors these days, the differences between an APS-C sensor and the next two sizes down are really not big (except maybe in dark conditions, and then much less than it used to be). And if you go to a slightly smaller sensor, you can do what Fuji and Sony have done (with the X10 and the RX100): make a very compact camera with high quality results, and still have a flexible and fast zoom lens, freeing up the usefulness of the camera enormously.
Size comparison from camerasize.com:
They are indeed almost the same size. The Nikon has a notch bigger sensor, but from the comparison shots on the article on top link, it doesn't seem to make a huge difference. The Olympus has in-body stabilization and exchangeable lenses.
It should be said, like Bru points out, that with most lenses, an exchangeable-lens camera become larger than a fixed-lens camera with a foldable lens.
Though in my view, as I've said, this needs to be a reasonable zoom (28-120mm) to be really useful. And for this to be compact, even folded, the sensor currently needs to be smaller than the one in either of these cameras.