Finally there are two Asus motherboards on my shortlist:
ASUS P6X58-E PRO and P6X58-E WS. There are unfortunately no reviews about ASUS P6X58-E PRO. My priorities are reliability and stability of MB.
Could you please give me some advices which model would be better?

Asus? Why don't you get a Supermicro board or something? Some server vendor should have products available in your country... but maybe they're too pricey. Supermicro is afforable in many countries when you compare their products to other board with expensive chipsets such as the one you looked at.

I always have used Asus for home computer and I trust them. I do not know Supermicro products. I just looking for very stable home computer.

Have you looked at Asus P8B WS (socket 1155)?

Is it really worth to consider p67 or Z68 instead of X58?

Not if you want stability. The PRO shouldn't be considered either. I don't know which Asus board would be best but if you want stability, get one like the WS which supports Xeons and ECC RAM. Generally, you can't call a desktop without ECC RAM "very stable".
And like I said, I'd get a board from a vendor which has a track record in the server market which is the market where stability is valued most. Most server vendors also sell "workstation" boards designed to be used as a desktop rather than as a server. Of course you could also get a "server" board for a home computer if it's got the features you want and isn't too expensive.