Our own civilization (arguably) dates to the Magna Carta. It has meant increased personal freedoms; it has meant increased economic freedoms; it has separated church from state; it has spread to many countries.
Islam cannot compete. It has produced no material wealth on its own. It has no living legacy of lawful, just, peaceful society.
Islam does it better. They can expand, but they are very seldom driven back. Spain was one of the few exceptions, and that took hundreds of years of bloody war and sacrifice to accomplish.
The Ottoman Empire fell because it couldn't match the material attractions of the West. But the pieces it fell into continue to be as Islamic as they ever were.