The modern world is more connected than ever possible before. Mass transit, international trade, illegal immigration, each spreads the world's people to different areas of the globe. With these things at a peak of effectiveness, it means that any form of disease can spread across continents and oceans with alarming speed. A disease which can control the infected victims and make them spread it (e.g. a zombie plague) will spread even faster.
For example, an outbreak could start in China, like in World War Z, then a visiting Canadian could get infected, return to Toronto, and infect thirty people on a subway. These thirty could then infect fifty at the station. The infected may cross the border into the US and spread the infection to Miami. The infected may then get on a cruise ship bound for Tahiti, etc.
Back in previous outbreaks, such as one during the Roman Empire, the infected had to walk to their destination. Plus, back then, every town had a local militia. A modern town is lucky to have a police station and a nearby reserve base. In ancient times, every able bodied man were encouraged to train for combat. Now, with the rise of the middle class and white collar workers, the bulk of the population of the First World would require military protection and retraining. Also, in ancient times the population was in the tens of millions, now it is pushing seven billion. The total possible number of infected would be almost a thousand times higher.
In short, a modern day zombie plague will spread faster and grow larger, and people will be worse off fighting it.