You can become a Jew by becoming a convert to Judaism. But you cannot become an Israeli just by moving to Israel. Jewry is primary, Israel secondary.
Also, due to Zionist influence it is not very well known that before Israel was set up as a state by secular Jews after Balfour declaration, in 19th and 18th century already a few groups of religious Jews from Eastern Europe had moved there on their own, to live under Ottomans. In Judaism it is forbidden that all Jews suddenly move to Israel, but a few can. So actually they were first there and they have a valid point now saying that we want to live here but not under Zionist regime. It is not like the religious Jews are simply ungrateful for the Zionist gift, because they already were there before Zionists and their design for Israel is different. You can be a Jew, live in Israel and not be an Israeli, all at the same time.
Since Israeli identity without being a Jew is essentially meaningless - as demonstrated by the lower social status of Israeli Arabs - I would say that Jews tend to identify as Jews rather than Israelis because it is their primary identity and Israeli only a second one. Also, because not all Israelis are Jews there could be an element of duplicity in such identification. This is also, I think, why two states solution rather than one state solution is more popular as a key to solving the Israel-Palestine problem
This duplicity element was demonstrated very well by the famous case a year ago in Germany when a young Israeli wearing kipa was assaulted by some Arab youths in a well-to-do district of Berlin, and no one helped him (this was actually the point why the case gained some notoriety). Everyone thought the victim was a Jew, and only a few days later it was announced the guy was actually the Israeli Arab.
And few months ago I was in Berlin and passing by the synagogue I noticed that it was protected by armed German policemen, but Arab looking ones, and who, with their big bushy beards looked almost like ISIS militants, just accidentally in the German uniforms. This was the only time during my week in Berlin when I saw Arab-looking policemen. Maybe Berliners like pranks... but if I were a Jew going inside, these strange guards would not really make me feel better. But If I were an Arab... maybe they would.
Also, due to Zionist influence it is not very well known that before Israel was set up as a state by secular Jews after Balfour declaration, in 19th and 18th century already a few groups of religious Jews from Eastern Europe had moved there on their own, to live under Ottomans. In Judaism it is forbidden that all Jews suddenly move to Israel, but a few can. So actually they were first there and they have a valid point now saying that we want to live here but not under Zionist regime. It is not like the religious Jews are simply ungrateful for the Zionist gift, because they already were there before Zionists and their design for Israel is different. You can be a Jew, live in Israel and not be an Israeli, all at the same time.
Since Israeli identity without being a Jew is essentially meaningless - as demonstrated by the lower social status of Israeli Arabs - I would say that Jews tend to identify as Jews rather than Israelis because it is their primary identity and Israeli only a second one. Also, because not all Israelis are Jews there could be an element of duplicity in such identification. This is also, I think, why two states solution rather than one state solution is more popular as a key to solving the Israel-Palestine problem
This duplicity element was demonstrated very well by the famous case a year ago in Germany when a young Israeli wearing kipa was assaulted by some Arab youths in a well-to-do district of Berlin, and no one helped him (this was actually the point why the case gained some notoriety). Everyone thought the victim was a Jew, and only a few days later it was announced the guy was actually the Israeli Arab.
And few months ago I was in Berlin and passing by the synagogue I noticed that it was protected by armed German policemen, but Arab looking ones, and who, with their big bushy beards looked almost like ISIS militants, just accidentally in the German uniforms. This was the only time during my week in Berlin when I saw Arab-looking policemen. Maybe Berliners like pranks... but if I were a Jew going inside, these strange guards would not really make me feel better. But If I were an Arab... maybe they would.