All we ever saw Kirk and Spock doing was playing chess.
O'Brien and Bashir drank, fought the Alamo, played darts, discussed women..
But Kirk and Spock were working with a huge culture gap and were friends. Bashir and O'Brien were from very similar cultures.
Oh believe me I'm all for Kirk and Spock and their deep bond. I think it's a soulmate kind of thing that transcends regular friendships. But what we saw on screen of Bashir and O'Brien was the stuff of human friendships that most people desire. Buddies, comrades, confidants, playmates.. and good point that there would be less of those activities because of cultural differences with Kirk and Spock.