Dry, cracked lips are often sensitive and can hurt if you apply pressure. A balm is softer and easier to apply because it is more spreadable. A stick needs a bit more pressure and so is more suited for occasionally dry lips that need a bit of extra moisturization now and then. However, first and foremost, it is about personal preference so you should choose the product that works best for you.
Eucerin Aquaphor SOS Lip Repair has been formulated to be used whenever lips send out SOS signals. The translucent balm has a pleasant ointment-like texture and comes in an applicator tube and so is easy to apply gently, evenly and directly to your lips.