Would acupuncture be better than seeing a chiropractor for shoulder pain?

Chiropractic is very new compared to acupuncture. Acupuncture has been around for hundreds of years but people react differently to treatments. Try both and see what you like better.

it did wonders for my lower back pain
I would definitely try a chiropractor first, these people do wonders with bones and muscles.
The only problem is that unless you know a good one you might get burned.
If the problem persist then try the acupuncture.
Personal experience.
There are several schools of chiropractic, some are the standard crunch and twist type...and others do more subtle adjustments. You might want to find an "activator" type chiropractor...I've seen good results from them.
But really...what is the cause of the shoulder pain? Do you have limited range of motion? Is it from an injury or repetitive motion?
You might be developing "frozen shoulder", which is usually caused by developing "trigger points" in the shoulder muscles. For that...acupuncture works well...but even better is "trigger point" therapy. You will have to do some googling to find "true" trigger point therapists...because lots of chiropractors claim to do it...but they really don't. Look for a trigger point therapist here... http://www.myofascialtherapy.org/...
http://www.myofascialtherapy.org/...
http://www.triggerpointbook.com/...
There are many possibilities to your shoulder pain.
A possible dislocation of your shoulder.
Bursitis
Encapsulitis
Frozen shoulder.
Your X-ray will reveal the nature of ailment.
Acupuncture is best for pain management. But then the underlying cause also has to be treated.
I am an acupressure therapist and as such treated a lot of frozen shoulder patients.
See a good acupuncture therapist and give it a try. There are no side effects.
Acupuncture is better than acupressure.
It is possible that your therapist may be able to cure the pain if he finds the right trigger points.