Which would be more suitable to combat migraines, reflexology or acupuncture?

As an experienced Reflexologist I have had clients who suffered from migraines and headaches for many years. After having reflexology sessions they reported to have cleared of these. As this therapy is non-invasive and involves more human touch I will go with it.
But without bias and never personally had Acupuncture I cannot comment.
At the end of the day it one's faith, connection between the therapist and the client, and the self-belief in becoming better and well.

Both therapies are often found to help; ensure that your practitioner is fully qualified, check them out and ask to see their qualifications and up to date insurance.
A good practitioner of either therapy will take a full history to get a complete picture of your migraines.
Reflexology may be more relaxing particularly if you are unsure about the needling aspect of acupuncture. One word of caution, don't have both - they are quite powerful! Whatever you choose stick with one or the other for a course of treatment coupled with any lifestyle advice given and see what happens. If you find no improvement, try the other therapy for a course. That way you will know what works best for you, and you will only be paying for one therapy at a time.