So YSK that the "is Zionism colonialist" question is laden with political overtones. Broadly speaking, a more pro-Israel person will deny that it was colonialist, and a more pro-Palestine person will tend to use that sort of terminology. While there is some bias there, I think it's mostly due to how Jewish settlement was seen by each group.

So from the Jewish end of things, you really can't call it colonialist. A key element of colonialism is that you're spreading the rule and culture of your native land to this new area. But that's not what Jews were doing. Not only was Jewish Palestine not trying to be subject to a European government, active rejection of European things was a substantial part of a lot of Zionist ideology. They were intent on creating a new society and having a homeland for their nationality, not spreading a European one. Hell, Jewish settlers were themselves from a substantial range of different cultures--French, German, Russian, and later on also from various Middle Eastern countries. There wasn't one European identity they were promoting, or a European country whose rule they were extending.

However, from the view of Arabs in the region it would've looked colonialist. People were coming in from a foreign country with a foreign culture. And they displaced people through being more powerful economically, and later on through violent conflict. If you're a Palestinian in the early 20th century, the part of colonialism that affects you is still present in the Jewish movement to the area.

This wasn't unacknowledged by contemporary Zionists, incidentally. Jabotinsky noted that the local Arabs would not acquiesce to Jewish colonization. He saw Zionism as colonial, but with the backing state missing, essentially. He noted the parallels with colonization elsewhere, that it was unlikely any colonized people wouldn't fight the colonizers. This text is The Iron Wall, if you want to give it a read.

But Jabotinsky wasn't voicing the unanimous opinion of Zionists. A.D. Gordon, for instance, saw diasporic Jewish communities as colonies of (then nonexistent) Israel, not the other way around. And note that he was talking about it being colonial with regard to the Arabs--I'm not sure if he saw it as colonial overall. Certainly the view of colonization isn't what predominated in Zionism, as most thinkers made it a great ideological point to point out the roots of the Jews in Palestine, to show that it wasn't just colonization.

Gingerkid1234 gives a good account, but I'd just like to add that not all differences can be attributed to colonialism (British or Jewish, if that can be called colonialism). The early- to mid-20th century for example saw an urbanization, population increase, drought and famish. Some of these are of course linked to conflict, such as the access to water. Colonialism might have escalated certain changes, such as through the reformation of education in the post-Ottoman era, boosting the influence of an urban elite. This is often, however, described as a positive aspect of both the Ottoman and British control of Palestine, they opened several new schools, introduced education for women, and provided the schools with modern equipment.

Sources:

Pappė, Ilan. A History of Modern Palestine (2nd ed, 2006) Cambridge: Cambridge University Press.

Fraser, T.G. The Arab-Israeli Conflict (3rd ed, 2007) Basingstoke: Palgrave Macmillan.