They both have claims to the land but I feel like Israel is more in the wrong because Palestine was the most recent one to occupy it legitimately.
A good place to understand this conflict is http://www.reddit.com/r/explainlikeimfive/comments/yh7dx/eli5_what_is_the_israelipalestinian_conflict/
I think you mean European Jews migrated there after the British Mandate ended. Jews have been in Israel for thousands of years.