A recent study in Germany showed acupuncture for chronic neck pain to be more effective than routine medical care. It was administered by physicians so the cost was more, too.
Another study from England had similar results using acupuncture for headaches. Most studies don't include patients with both headache and neck pain in order to avoid too many factors.
Some of your decision may depend on the cost of each acupuncture session in your community. Sometimes acupuncture is performed by anesthesiologists or other highly trained physicians. The cost is likely to be more than when acupuncture is done by a nonphysician such as a nurse or layperson.
If you can get the results you want in a short amount of time, then acupuncture is likely worth the extra money. If the treatments extend beyond a three-month period of time (two to three sessions per week), then the cost may increase more than the benefit.