AviraDeArah:
There are a number of very big differences between the two.
Eisav sonei liYaakov is axiomatic, but its practical application depends on, essentially, the degree of separation between Klal Yisrael and the umos. That’s what the Beis HaLeivi wrote on “hamavdil bein kodesh liChol, bein or liChosech, bein Yisrael laAmim…”.
As Rav Miller Zatza”l wrote, before the war, you had whole towns that were frum that became haskala towns. Numerous -isms, including, of course, Zionism, ensnared numerous Jews in their heretical nets. The Satmar Rav wrote how gedolim in the years before WW II said it would be a miracle if something did NOT happen to the Jews there.
Since WW II, however, almost everywhere, there has been an enormous tidal wave of recovery from the war and return to Torah. In the US, for example, the Torah landscape is massive relative to the little that existed before and immediately after WW II.
The only exception is, of course, the Zionist State of Israel, which shmaded and continues to shmad at least three generations now, though some of whom (but certainly not all) have come back to the Torah and, despite the Zionists’ many evils, there are many yeshivos there.
So, if your concern is safety in galus, you probably do not want to be under the Zionists which Rav Elchonon Wasserman called the worst galus of all, the galus of the Yevsektzia. Particularly when looking at a pig-eater like Yvet Lieberman, this becomes all the more apparent, though that applies similarly under the prior atheist Zionist Prime Minister Milikowsky (AKA “Netanyahu”) and all the others that preceded the pseudo-kippah wearing current Zionist PM.
Any claim that Israel is a “safe haven” for Jews is not only delusional but also simple Zionist idolatry. The Zionist mess, on every level, including both spiritual and physical, in the portions of E”Y that they have invaded, are nothing to envy.