Hannah Arendt's book Eichmann in Jerusalem contains a very readable nation-by-nation survey of what went on in Europe during the Holocaust, and (to the extent possible) why. Denmark, e.g., was the only nation to make a determined politically based resistance: the Danish Jews were "Danish citizens of the Jewish faith", and as for the refugee Jews in Denmark at the time, Germany had declared them stateless and so could not expect to get them back.
Everywhere else, statelessness was damaging to Jews, but in Denmark, where the government had decided to protect the Jews, it paradoxically became an advantage. The story of the yellow star (if the Germans imposed it on the Jews, the King of Denmark would be the first to wear one) is probably apocryphal, but it sufficiently indicates the attitude of Danish citizens of all classes of society.
It turned out that the one and only time that the Nazis met resistance of this kind, they collapsed under it absolutely: it is very possible that the Danes were warned of the coming German roundup of the Jews (which found only about a hundred too old, too sick, or too isolated to hide) by a member of the German embassy in Copenhagen.
In Italy and Bulgaria, it was more a matter of humanitarianism. Although they were officially allies of Germany, all the preliminary moves required for the Final Solution were mis-executed, bollixed up, ignored, or (in one case) flatly refused "as inconsistent with the honor of the Italian Army".
In Arendt's view, Western political Antisemitism in general was a response to the general conditions after World War I, where the rich Jewish banking families were percieved as having prolonged the war to their own profit by lending money to both sides. In one of those switches all too common in history, a group earlier praised by cultural leaders for its cosmopolitan and pan-European attitude was now condemned for being insufficiently nationalist. (This is distinct from the social Antisemitism, centuries old, which was at the time rapidly declining in Western Europe.)
In the East the problem was different: the general settlement after World War Ihad to take into account the collapse of the Austro-Hungarian and Ottoman empires. The vast belt of mixed populations was then carved up in such a way that some groups (Serbs, e.g.) got their own countries and others (Croats, e.g.) did not, with consequences visible a century later. The Jews, although found everywhere, were nowhere in the majority, so it was impossible to create a Jewish autonomous region in any of the new countries. Therefore, the Jews (who were recognized as a distinct people by everyone, as opposed to the Western situation where "it was considered a sign of Antisemitism to call a Jew a Jew") ended up consistently on the bottom of the pecking order, blamed for everything that went wrong.
But read the book. This potted summary of a tiny section does not do it justice.