Fillers or Dermabrasion for Lines Above Lips?

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.

Upper lip wrinkle lines can be improved with fillers such as Juvederm and Restylane. The correction should last about 9 to 12 months. Usually it is advantageous to add filler to the borders of the lips as this helps efface the lines in these areas and can also provide fullness for the lips.
Adding Botox will diminish the active wrinkling caused by the movement of your lip muscle and can enhance the result though not everyone likes the "feel" of Botox in the lips, and the Botox only lasts about 3 to 4 months. Dermabrasion can significantly reduce wrinkle lines and provides a more permanent correction.
Adding fat grafting improves the result, and can provide fullness for the lips if desired. Some doctors feel that the stem cells in fat grafting will help "restore" the tissues to which the fat is added. The results of fillers are immediate and there is minimal downtime. Botox takes 2 days to 2 weeks to be effective. Dermabrasion is a surgical procedure and has significant downtime of 7 to 14 days. Fat grafting looks overdone for about 2 weeks. Many times, dermabrasion and fat grafting is done at the same time other facial rejuvenation procedures are being performed such as face and neck lift.

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.

Easy answer is use very temporary fillers (Restylane, Juvederm) first. There are simple to inject, last 3 months, are inexpensive. If after a trail with the temporary fillers you can proceed to a semi lasting filler (Perlane, ArteFill). Dermabrasion is a surgery that has healing time of 2 weeks to months, and is much more expensive.
The basic physiology of upper lip wrinkling:
1. Loss of volume in dermis or a thinning of the tissue causing a valley/crater appearance;
2. muscle hyperactivity;
3. a combination.
So the treatment is either fill the valley with a filler or fat vs sanding down the hills of skin on each side of the valley (vertical lines) in the lip. Hope this helps.

The answer depends on the amount and depth of the lip lines.
Many lip lines are vastly improved with fillers. I strongly recommend you stay away from "permanent" or semi-permanent fillers because these terms describe their potential complications more than their pleasing results. Hyaluronic fillers either Restylane or Juvederm have a satisfactory track record and produce good results.
Dermabrasion like chemical peels have rapidly of historical interest only. Better and more predictable results can be produced with certain lasers. I encourage you to look into Sciton Profile or Joule Erbium laser and its LASER MICROPEEL, PROFRACTIONAL and CONTOUR TRL. These modalities will greatly improve your appearance.
Dr. P. Aldea