I've heard other street/prison gang members explain this, but in a slightly altered way. It's not that the Mob is disrespected in prisons. It's just that they stick to their own.

Inside is a different world than the one outside and traditional organized crime has a different business model than street gangs have. Traditional organized crime wants to make as much money as possible with a select amount of people, which in turn makes them very selective organizations. Their game is focused on earning and staying out of the can. Street gangs on the other hand aren't selective at all; quite a few gang members make money (from very blue collar rackets, but they still earn), but WAY more members are just in it for the "clout". For a lot of these gang members going to prison is a badge of honor.

So in turn - when we use East Coast prisons as an example - the number of traditional OC guys in prison is going to be comparatively small while prominent street gangs like Bloods, Latin Kings, Trinitarios, DDP's...are going to have HUGE numbers in prison. Of course numbers are gonna run the yard in prison. Where does that leave the others? They're just gonna try to stay out of trouble and stick to their own. That's the case for the Mafia, that's the case for the bikers and that's the case for other smaller ethnic organized crime groups (Russians, Chinese, Albanians...to name a few). They don't have any interest in (nor would they have the numbers for) "splittin' wigs" and running the yard.