The plain Latin cross is primarily a "simplified" crucifix. Christianity has a long history of different cruciform symbols with various degrees of meaning.
One could see the use of a plain Latin cross as a vacant cross--the Son of God taken down from the cross, laid in the tomb, and having risen from the dead. And that is a beautiful symbol. I love that symbolism.
The crucifix specifically calls our mind to Christ's passion and death, His work of atonement. Which is why it often features prominently in Lutheran contexts as Lutherans see ourselves as "Cross people". Luther once said in his 28 Theses of the Heidelberg Disputations that a true theologian does not understand God in His invisible qualities of glory, power, and wisdom; but in His visible revelation: In the Incarnate Jesus Christ who suffered and died for us. To know God in God's suffering on the cross is the mark of a true theologian: I.e. God is not defined chiefly in abstract concepts, but rather is defined by Himself in His Word Incarnate, in the Incarnate Person of Jesus Christ our Lord.
In the East a more common symbol is the Christus Rex:
The Risen, Glorified Christ superimposed on the cross showing His victory over death and the grave. Christ is King, the King who rose and has conquered sin, death, hell, and the devil and is ascended and seated at the right hand of the Father. The Crucified-Risen King who lives forever.
All of these are beautiful symbols of Christian faith. Though I do admit that the traditional western crucifix is often what resonates most deeply with me--as I am drawn visually into meditation and contemplation over the Savior's loving Self-offering of Himself for me, a wretch and sinner. That I do not know God in power or wisdom, in sagacious philosophy and human reason, but rather I know God in Christ Crucified. He died for me, an ugly unlovely sinner, deserving of death and hell.
1 Corinthians 1:18-31 - 2:1-5
