Did pain fellowship, I think it makes you slicker with things like needle insertion, blocks, local anesthetics, can help with outpatient opioid management in pacu for pain patients, save a pain consult kind of thing, promote new concepts like multi-modal analgesia. It certainly does not improve your bare essential anesthesia skills like airway or vascular access that CCM would. But i certainly would say I feel more like the bottom line, expert, being a board certified pain specialist when talking about a perioperative pain management plan, talking about the best way to do cases for long term outcomes, and for having my needlesticks hurt less than the next guy I have learned subtleties in performing block procedures over and over that make me the guy you want doing your block and not the guy who did the ccm fellowship, trust me. I think as far as being in the OR and basic anesthesia skills who you are as an individual and how you did in residency are the biggest predictors of overall badass-ness, neither fellowship helps that part. but i would in the end agree with the above in that if you dont want to do a lot of practicing chronic pain, dont do the fellowship, its not worth it.
and as far as actually doing the pain blocks: you absolutely need a fellowship to learn to do proper pain injections. a general anesthesiologist i would be surprised if they could locate the facet joint on xray.