Well, ignoring any religious meaning here, and just basing everything entirely on the known text, the Jews have actual history in the area which the Muslims don't have (but they desperately want to pretend they have).
Ignoring any religious context in general, Islam is not a peoples, it's a religion, while the Jews are both. If you're going on ethnic claims, the Jews muscled out the Eblaites, literally the oldest coherent multi-city civilization ever recorded, with much of the region devolving into city-states for centuries to follow. With religious context, Genesis describes the peoples that the Jews are muscling out to acquire their fated homeland in detail: the Kenites, Kenizzites, Kadmonites, Hittites, Perizzites, Rephaites, Amorites, Canaanites, Girgashites and Jebusites. Despite proclamations against intermarriage, the Kenites and Hittites especially were integrated into the Jewish people, while most of the rest were expelled or enslaved.
Syrians are particularly the Perizzites (generally considered to be the oldest group listed) and much of the Canaanites, with the order of dominance in what is modern Israel seemingly going Perizzites->Jebusites->Hittites, with various regions split between the Girgashites and the Amorites nearby.
Leaving ancient history, the Jews lost the Levant to Syrians again, and then to the Romans, and eventually Arabs, and Arabs have owned it the longest (again, excluding ancient Syria). Christians have the strongest non-Arab claim to Jerusalem, IMO, the Kingdom of Jerusalem held down the fort far longer than modern Israel has managed yet, and Cyprus for ages after that.
In 500 BC, when the Jewish Maccabees were (already) rebelling against Macedonian occupation, the Arab Nabataeans to their south were making the most wealthy country on the entire planet, complete with a crazy fort-castle-trade-city made out of hewn stone. The Maccabees in fact received significant support and protection from the Nabataeans at the time, proving that eventually old relationships and contracts can in fact be "too old to matter." In terms of claims to land or kingdom, Jews would not be my first bet. That's why they need to be busy selling people on their continued presence in the region.
