A strstream builds a char *. A std::stringstream builds a std::string. I suppose strstreams are deprecated becuase of the potential for a buffer overflow, something that std::string automatically prevents.
Easier to understand memory management. (Can someone remember who is responsible for freeing the allocated memory and in which conditions?)
(Note that as strstream still provide something which is not available elsewhere, it will continue to be present in C++0X -- at least last time I checked the draft it was).
The strstream returned a char * that was very difficult to manage, as nowhere was it stated how it had been allocated. It was thus impossible to know if you should delete it or call free() on it or do something else entirely. About the only really satisfactory way to deallocate it was to hand it back to the strstream via the freeze() function. This was sufficiently non-obvious, that lots of people got it wrong. The stringstreams return a string object which manages itself, which is far less error prone.
There was also the issue of having to use ends to terminate the string, but I believe the deallocation problem was the main reason for deprecation.
From a personal perspective on more than one occasion I've seen obscure memory corruptions that took days or weeks to track down and eventually came down to use of strstream. As soon as it was replaced with stringstream the corruptions vanished and I didn't ask any more questions! That was enough for me.