Kerbros is very extensive and for systems requiring high security. Its very difficult to work with, and even just setup over all, I would not suggest this route unless you know linux very well, and provided your hosting provider allows you that type of access over the machine.
Im not familiar enough with JOSSO or openID to comment well on those however.
Any php sessions are only good for the domain, and server the domain is on, kind of like cookies but not, though in all you would use them.
I think your easiest solution more so if the 2 sites are on the same hosting account/server. Is to have a database specific to this cause. What you would do is create a login system like you would normally but instead you would have 2 sites reading off this login. Aside from the normal login you would also have a session tracking table. Typically you already set sessions when users login to keep them logged in, and you'd do the same here, but you'd add a cookie into the equation one both sites can recognize and use to compare entries in this new table where your tracking your users. I'd say keep try by IP, Browser, and maybe a userID all in one cookie with a unique hash of some kind as well thats specific to the user based on something only the servers could recreate on the info they have for the user.
Of course I dumb it down in conceptual speak, its a little more elaborate than I make it out to be, but this would be your general stepping stones.
Also if the sites are independent of one another you could always create an API between them to pass info back and forth JSONP style so one can act as the hub for the login while the other just validates
But in all its all dependent of what your wanting to do overall how, when where, etc..