Fillers or Dermabrasion for Lines Above Lips?

I assume you mean aging lines of the upper lip. There are probably as many ways to treat this effectively as there are doctors. Each modality has its pros and cons. Chemical peels and dermabrasion have been used for decades with good results. Since the introduction of lasers in the 1990s I prefer to use laser for this. The major con to chemical peels, dermabrasion & lasers is that the cause some depigmentation in the course of eradicating these lines. If you have a baseline dark complexion you have to be very careful and it may be better to avoid these modalities in such cases.
My preferred choice is a CO2 laser and I use a needle to separate the depths of the folds from the under lying muscle. These allows me to do a little less lasering and is especially important with smokers as they develop a lot of scar tissue between the skin and the muscle on the side that they hold their cigarettes. With this approach depigmentation has been less of a problem and I only do this on lighter skin colored individuals.
I do not like injectable fillers in the lips because they are temporary and have a tendency to form lumps due to lip motion.
I will post a photo of this on the RealSelf website.

Hey there!
You have a number of choices here however much dependant on depth of the lines:
Botox for perioral lines relaxes the muscle that surrounds the mouth and is effective for dynamic lines - or those that appear when moving your mouth (not at rest)Soft touch of filler - to soften deeper / static lines that are present when not moving the mouth muscles Dermabrasion techniques are not my area of speciality but most that I am aware of required multiple treatments.
Make sure you see a fully trained aesthetic practitioner who can give you honest advice in which would be suitable for you. 
Hope this helps! 
Best wishes, 
Dr Rupert

The lines above your lips may have several causes. Treatment requires assesing the factors that play a role in the development of these lines. This may include:

repetitive motion or pursing of the lips that occurs with smoking or facial expression. In this instance botunlinum toxin (dysport) could be very useful.
involutional changes of the soft tissues are best treated with volume fillers such as Restylane
Superficial wrinkles "lipstick bleed" lines may respond to superficial fillers such as zyderm or mechanical treatment with dermabrasion or chemical peels.
loss of bone volume or dentition in which case dental orthotics or implants may provide additional benefits.

There may be other causes and treatments that suit your unique condition.