If Palestine got to have its own recognized (by everyone including Israel) and sovereign state, what other different current nation would it most likely resemble?
EDIT: I'm interested in how a free Palestine would play out in terms of what that would mean for women, gays, children, people of non-muslim religions, in terms of personal freedoms, etc. For the average citizen/denizen what would that look like?
Hamas, which is an fundamentalist, religious and military organization backed by Iran. If they were to gain power in a Palestinian state, it would look something like Hezbollah controlled areas in Lebanon. So... not good.
Fatah, on the other hand, is a (relatively) secular organization that's in good relations with western countries. If they were to gain power, Palestine would be more open to western influence, and will probably treat women, secular people and minorities better. This version of Palestine will probably be the most pro-western Arab state, so it might be more influenced by western values more than other Arab states. Of course, in the mid- or long run it's possible an extremist power will rise regardless of western backing (ex. Iran).
Assuming a you're talking about the near future, which organization will have control largely depends on if Hamas would exist. If so, they'll probably get the credit for a recognized state due to their "resistance". Then again, it's very possible one of the conditions for a universally recognized state will be the elimination of Hamas as a political (and obviously military) force.
I'm kinda ignoring the "including Israel" part of your question, as Israel would absolutely not accept any version of Palestine with Hamas.