The difference is yeast. Not whether or not it's used, but the specific type. But from this relatively small variant comes a whole slew of changes and differences that make these two beers very unique.
Ales - Ales are brewed with a top-fermenting yeast that thrives at mid-range room temperatures. For this reason, ales are typically stored between 60° and 75° Fahrenheit during the fermentation stage. This type of yeast and the fermentation temperature tend to give ales a fruitier and spicier flavor than lagers. In general, ales are more robust and complex. Common styles of ale include pale ale, India pale ale, amber ale, porters, and stouts.
Lagers - By contrast, lagers are made with bottom-fermenting yeast that work best at cooler temperatures, between 35° and 55° Fahrenheit. Fermentation happens more slowly and the beer is more stable, so it can be stored (or "lagered") for longer than ales. This yeast tends to have less presence in the finished beer. As compared to ales, lagers have a cleaner and crisper quality with emphasis on the hops and malt flavors. The lager family includes pilsners, bocks, and dunkels.
Is one style better than the other? Definitely not. It's all a matter of personal taste or what we're craving at that particular moment. Personally, we love all beers equally - just so long as they're good!
Do you have a preference for ales or lagers?