The correct statement that accurately compares and contrasts the Palestine Liberation Organization (PLO) and Hamas is:
Although the PLO and Hamas are both in conflict with Israel, the PLO has recognized Israel's right to exist, while Hamas wants to eliminate Israel.
This statement captures the fundamental ideological difference between the two groups regarding their stance on Israel, with the PLO having accepted a two-state solution and recognized Israel's existence, while Hamas does not recognize Israel and seeks its elimination.