Should you take pills or use patches for pain relief?

Pills and patches reach the body differently, and they are priced differently too. Which one suits you is a clinician's call.
What patches offer
We cannot pick one for you, but Wikipedia lists an advantage of patches. An advantage of a transdermal drug delivery route over other types of medication delivery (such as oral, topical, intravenous, or intramuscular) is that the patch provides a controlled release of the medication into the patient, usually through either a porous membrane covering a reservoir of medication or through body heat melting thin layers of medication embedded in the adhesive.
What kind of patch is meant
Not every patch is mild. Wikipedia adds a caution about strong ones. Two opioid medications used to provide round-the-clock relief for severe pain are often prescribed in patch form, fentanyl CII (marketed as Duragesic ) and buprenorphine CIII (marketed as BuTrans ).
Compare the same dose period for each, such as a month, and ask what the price includes.
What to do next
Ask your prescriber why one form is proposed over the other and what the monthly price would be. For background, read the MedlinePlus chronic pain page, the NCCIH review of chronic pain approaches and Healthline's guide to the causes of chronic pain.
Pricing pills and patches on the same footing
A price per pill and a price per patch are hard to compare. In Garfield or anywhere else, ask for both prices over the same dose period before you decide.