Jews are called to be an example of God's people to the Gentiles, and to live in the Promised Land. They are not particularly called to spread their religion.
Christians are called to spread the good word of Jesus over the whole world, so everybody has a chance to accept or reject Him.
Muslims are called to spread their religion first by persuasion backed by military force. Governments that refuse to submit are to be overthrown. The new Muslim governments are called to graciously allow for an oppressed class of people who still want to practice Judaism or Christianity. The rest of population must convert or die.
Actually, Mashiach will "compel" (Rambam's word) the nations to observe the Noachide Laws, which are as statutorily obligatory on non-Jews as Halakhah is to Jews.