I always thought that first variant (both letters written uppercase) is appropriate (maybe because I'm a Windows user), but recently I see more usages of second one (only first letter written uppercase). Which one is more eyes- and mind-friendly?
Stick with is most common and time-proven. OK (with caps) has been used always. You can see its wikipedia page, is written using both caps.
It's also worth thinking about how the appearance would affect someone reading aloud. OK is recognisable and forces a break between the letters ("oh kay"), while I've seen people slow down as they remember that Ok is the same thing and isn't "ok" or "och".
There's also the pedantic answer to consider.
All dictionaries I am aware of list OK as the correct spelling for the word, never Ok. (In fact, the StackExchange spelling checker even flagged Ok as an error.) So Ok simply means you have a spelling error. One of the other comments mentioned practice in Denmark. I'm assuming we are discussing English, either US, UK, or some other major variant.
It is acceptable to use okay in written language, although Apple's documentation guidelines require the use of OK (search for "okay"). Most human interface guidelines that bother to point out the obvious say specifically to use OK in a button, though, not okay. See for example the Microsoft guidelines.
Finally, as a matter of clarity, a lot of sources now suggest not using an OK button at all, but replacing it with something more descriptive. See for example this article. It's not bed, despite the fact that the author didn't know how to correctly spell a key word in the title. :)