Something to think about!
If you are in the market for a new lawn mower this is a common question to ask. The tractor mower has been the most common riding mower up until the past decade or so. Some people have stuck with the old faithful tractor mower because of tradition and comfort.
You typically set higher on a tractor mower and they most always have a small place to hitch pull behind equipment. The zero turn typically has a lower center of gravity and roll bar making them safer on small slopes. Neither riding mower is recommended for slopes greater than 45 degrees. These slopes should be push mowed or different equipment should be used.
The main difference with the zero turn is the deck typical sets in the front under your feet, while your steering is done with two independent drives controlled by your hand levers which allows for much easier and quicker turns. This feature is what makes the zero turn the most popular mower in recent days. With such turn accuracy and maneuverability around buildings, trees and landscape, much of your mowing time is shaved off. You rarely ever need to use reverse and if you do its as simple as moving the hand levers backwards instead of having to change gears.
Both tractor mowers and zero turns have increased there speeds in recent years but there are many more options for engine sizes, speeds, decks and other features on the zero turn, while typically being the more expensive of the two. It all boils down to personal preference, price and how much time you want to spend mowing your lawn. Cheaper price is typically the tractor mower. Zero turn typically more expensive, faster and definitely quicker to maneuver around lots saving you time. Why more and more people have switched to the zero turn mower.
Hope this answers some questions or concerns you have before making your new purchase!