What If Alexander the Great had gone West and not East?

I stumbled across this archive of and interesting BBC Channel 4 radio show originally broadcast in 2003.

History - Radio 4: "Imagine if, one hundred and fifty years before Hannibal, Alexander moves his army around the North African coast of the Mediterranean, conquers Carthage, and crossing at Gibraltar takes Spain, crosses the Alps, and easily subdues what in the 3rd century BC was the relatively ineffectual army of the Republic of Rome, then still a mere city-state.

What kind of world would that have given rise to, a Europe with a Greek rather than a Roman legacy? What would its legacy have been?"