We have both empty crosses and crucifixes in our churches -- each has a meaning. Marmema is right, though, that most of the time the cross that we wear on our bodies everyday is an empty one.
"When you see a poor wooden Cross, alone, uncared-for, and of no value... and without its Crucified, don't forget that that Cross is your Cross: the Cross of each day, the hidden Cross, without splendour or consolation..., the Cross which is awaiting the Crucified it lacks: and that Crucified must be you." (St. Josemaria Escriva, The Way, 178)
"You ask me: why that wooden Cross? — And I copy from a letter: 'As I look up from the microscope, my sight comes to rest on the cross — black and empty. That Cross without its Crucified is a symbol. It has a meaning which others cannot see. And though I am tired out and on the point of abandoning the job, I once again bring my eyes to the lens and continue: for the lonely Cross is calling for a pair of shoulders to bear it.'" (St. Josemaria Escriva, The Way, 277)
Like I said, the Latin Church is the Church of the Passion, the Eastern Church that of the Resurrection. Both important, both the "sin qua non" of The Faith, but the emphasis speaks volumes on what we each are about.