These methods are great for someone who wants to go lighter or add some dimension to their hair, but wants less maintenance than having foils. Both techniques transition from dark to light, so your regrowth can be much less noticeable.
Balayage is generally a more subtle effect and does not necessarily require all the ends to be lightened, with a particular focus on the top layers of the hair. The transition between dark and light will be much longer and more natural looking, mimicking a sun-kissed or naturally lightened hair.
Ombre is a lot less subtle and creates a much lighter appearance on the ends of your hair. Generally, all of the ends will be lifted, creating a much more dramatic transition from the deeper roots to the lighter ends.