Self-propelled mowers are meant for yards that have slopes, since they are powerful and have various speeds. The adjustable speeds allow you to choose a comfortable walking pace as you mow. Push mowers work best with lawns that have little to no slope, since they have much less power than self-propelled mowers and require you to do most of the work.
Self-propelled mowers are preferred for large lawns because they require less energy to push them. Push mowers also work with large yards, but are more convenient for smaller yards since you don't need a lot of power to mow a smaller yard.
Self-propelled and push mowers also vary in cost. Self-propelled mowers are more expensive than push mowers, costing upwards of $900, while push mowers average around $200, according to a 2006 article on All About Lawns.