I have currently the D300. I am debating whether to upgrade to the D600 or the D800. Here in the UK the price difference is about £300-£400 depending on store.
So spending £1650 or £2000 isn't that difference really...
So like you I went into a couple of camera shops here in London and handled them both.
Both appear to be good cameras, fitting well in the hand etc. However for me the D800 felt larger, heavier (in a good sense) and the controls appear more similar to my existing D300. The D600 was slightly different in the ergonomics of the controls.
As such I am likely to get the D800 as it suits me better ergonomically.