There are certain similarities, but they are difficult to compare. Zionists and Palestinians both believe the land is promised to them biblically and in the Koran. They believe they are being oppressed by an unlawful occupier (Britain for the Zionists, Israel for the Palestinians). Both have resorted to guerrilla warfare to achieve their goal of independence.
This question is impossible to answer in an even-handed way. It is one that is totally caught up in how one feels about Israel and the Palestinians. I'll try to be factual, but any analysis is sure to be biased:
- Zionism wanted a land for a people who had none of their own. The Palestinians at least have other nearby countries run by coreligionists who are ethnically similar to them.
- Zionism achieved its goal after the Holocaust had showed what some see as the necessity of having a Jewish state. Nothing like the Holocaust has ever been done to the Palestinians.
- On the other hand, Israel was created by taking land away from people who were currently living on that land. It was done largely because powerful countries felt kinship with European Jews much more than with Arab Muslims.
- So the Palestinians' struggle is rooted in a much more recent wrong that was clearly done to them by the Israelis and their supporters.
So the Zionists had endured much more abuse over the years before that State of Israel was created than the Palestinians have since. They were in a much worse position in terms of what could and had happened to them.
On the other hand, they took land from those who lived there and who had done nothing to them (the Zionists) that would deserve punishment.
So it's really hard to say if the Palestinians' moral claim on the land is stronger than that of the Zionists or not...