Answer:
This depends on what you would like a solution to maximize. (I.e. do you want the greatest stability, do you want to give into one side's demands more than the other, do you want international interference or not, and forth.)
Arguments for a Two-State Solution
1) Long-term Stability: Giving the Palestinians and Israelis each a state where they could govern their own populations according to their customs and traditions would be better for long-term stability than a Jewish Police State (to which the Palestinian Territories currently belong) or an Arab Police State (which was seen in fits and starts as concerns the Jews during and after World War II). If each side has a modicum of privacy in which to take care of its internal affairs, violence will be less likely.
2) Democratic Jewish State: There is a saying in Israel that goes as follows: Israel has three things: Control of the West Bank, Democratic Government, and a Jewish Identity, but it can only have two. That is to say that Israel can control the West Bank and be democratic, but that will result in an Arab State or Israel can hold onto the West Bank and its Jewish Identity, but that will only be achieved through an apartheid state apparatus (a number of people think Israel is trending this way) or it can remain a democratic Jewish State if it forfeits the West Bank. Many Israelis and many Jews outside of Israel would rather relinquish the West Bank than see the democratic or Jewish natures of Israel disappear.
3) Bilateral Economic Partnerships: Israel and Palestine used to have an incredibly interdependent economic system where a large number of Palestinians used to commute to Israel for work and go back to Palestine. This intercultural exchange liberalized a lot of Palestinian attitudes towards Israelis and vice versa. With a one-state solution where that state has a Jewish character, the animosity between occupier and occupied will prevent this from working. With a one-state solution where that state has an Arab character, many Jewish business leaders will be very skeptical about staying because Arabs have confiscated Jewish property and jobs previously (in Iraq for example).
Arguments Against a Two-State Solution
1) Invasion has no Statute of Limitations: Many Palestinians and even more Arabs hold to the view that the Jewish people stole Palestinian territory and used that land to found Israel. In their eyes, the existence of anything but a Palestinian State in that territory is allowing the atrocity that occurred to the Palestinians to persist.
2) Jewish-Arab Mutual Project: Some one-state solutions have been proposed to create a State with a bi-national character. That is to say that the State would be Isratine (for wont of a better name) and Isratine would be broken up into districts that would declare if they were Arab or Jewish. Depending on which one they chose, they would be subject to the Arab or Jewish laws respectively. Proponents say that this type of plan is good because it allows for demographic changes to leave the fabric of Isratine intact. Detractors say that this system is prone to gerrymandering, fraudulent voting, forced relocations/retaliations, and confederal jurisdiction issues (i.e. if an Arab attacks a Jew in Arab territory can he be sued in an Arab court or a Jewish court or a special national court?)
3) The Arabs Have a Home: There are a number of Religious Zionists and pro-Israel advocates that note that Bilaad Sham, the ancestral ethnic region to which Palestine belongs, already has three independent Arab Nations sitting upon it (Jordan, Syria, and Lebanon). Considering that the Palestinians could theoretically move to these countries and be under laws similar to those that they would implement in Palestine, they would ask why it would be necessary to accommodate another Shamite State by ripping holy territory away from Jews?