Neither is better in every case: it depends on the door and what you are after. A mortice lock sits inside the door leaf; a surface mounted lock is screwed to the inner face.
Mortice. It is the usual one on house doors and security doors. It looks neat, protected inside the door, and is worked with the handle and the key. It needs a door that is thick enough.
Surface mounted. It is fitted on the inside, without cutting into the door. It is very useful as a second lock, above the main lock, and on thin doors, storeroom or warehouse doors, where a mortice lock will not fit.
What many people do is combine them: the mortice as the main lock and a surface mounted deadbolt as reinforcement. We help you choose in lock installation.