Antisemitism in Europe was traditionally more intense than antisemitism in the Islamic world. So why did Europe host a larger Jewish population for most of its history?

I'm no expert in Judaism in Europe, but having studied Modern European history quite a lot I think I can answer this question for you. When people think of antisemitism, they often think of Nazi Germany. The powerhouse of Jewish oppression and elimination. But, to understand why this is, we need to look back to the centuries following the Renaissance. In Europe at that time, the HRE was still a dominant political force, and although there was no German nation, there was a common ideology, as in most European nations; to clarify, I define nation as a group of people with a common ideology and culture, not what we would refer to as a country, which is really a nation-state. France functioned similarly with an equal hate of Protestants and all other religions, as did England and Spain, as we saw with the Spanish inquisition.

Now the role of Jews in smaller nations is where we see an emergence in Jewish culture in Europe and a growth in population. Although there was much discrimination in larger nations like those I mentioned above, many rulers saw discriminated populations as a way to grow. But, this creates another level of complexity. To address this, I'll use the Spanish Netherlands as an example. During the rule of Philip II, all 17 provinces of the Netherlands were controlled by Spain. Naturally, the Netherlands hated this, especially when Philip sent the inquisition to eliminate all protestants from his territories. During this time, a tremendous population of the European Jewish peoples moved themselves into the Netherlands, a nation which was incredibly open to other religions, as were other small nations such as Switzerland and Brandenburg. The leaders of these nations saw opportunity in well education immigrants, effectively opening their doors to everyone. They largely left the Jews alone and let them work and thrive in peace, while creating incredible economic benefits. Then all of a sudden, when Spain decided they wanted everyone but the Catholics out of The Netherlands, the Jews were already a part of this unified Dutch culture, and rose up to fight against Spanish oppression, with the help of our good friend Louis XIV. But that's a story for another time.

So essentially, oppression was only common in larger nations who were unified predominantly by a shared religion, and not a good leader, but an absolutist one. France under Louis XIV was not good, and Philip bankrupted Spain five times over the course of fifty years, but what kept Spain together was Philips rampant Christian ideology. Smart leaders saw more people who needed a safe place to live, and capitalized on that, it's really quite simple.

Now in regards to who got to Europe and how, we look towards the Crusades. This period of time saw migration of both European and Middle Eastern peoples to each others regions, which is primarily where we see the Jews move around. The Ashkenazi, although beginning their development in the HRE in the Middle Ages, had moved east into Poland and Lithuania by the early beginnings of the Renaissance, and like other small nations, greeted them with open arms. The remaining Ashkenazi experienced forced assimilation and lost much of their culture. Mizrahi Jews on the other hand did not migrate to Europe in the numbers that the Ashkenazi did. Instead, they moved themselves to Asia and India some nations in the non-Muslim Arab world.

If you want to read more about the migration of Jewish peoples into various European nations I would recommend Torquemada and the Spanish Inquisition by Rafael Sabatini, which takes a very factual look at the centuries of oppression. Living Together, Living Apart: Rethinking Jewish-Christian Relations in the Middle Ages by Johnathan Elukin is also quite good, and addresses a larger portion of your question.