I am only a couple years into practice, others in this forum have far more experience than I do and I would be happy to hear from them
Just depends on how greedy you are. An anesthesiologists doesn't need to work for patient referrals or reach a specific benchmark to receive a salary bonus. Therefore recent anesthesia graduates typically have a higher salary close to $50k more than pain jobs because they don't need time to grow their practice and therefore overall revenue. There are anesthesia job with and without call. Call usually pays between $1-1.5k in most places in addition to the higher salary. This can add up to an additional $50k salary.
However, the trade off is lifestyle. Pain has a very predictable work hour and very flexible to your needs and desires. For example, my hospital allows me to hold office hours from 9am-7pm on some days so Fridays I can work from 9am-12pm. I have no weekends so its almost like a 3 day weekend every week of the year. In anesthesia, your hours and holidays are at the discretion of the group. If you have a birthday party or wedding you want to attend to you will have to plan months in advance and trade weekends and days with other attendings like in residency. Also, you are respected at a pain job by both the patients and the staff. You are the doctor and you call the shots! I still call patients at home if they miss their appointment and check up on them because I want to. You build a connection and feel amazing when they do well.
I never joined a private practice group because it was hard to find one I really liked. Most of the private groups I liked were affiliated with a local hospital so I took that as a sign. The more desirable locations were oversaturated by neuro pain, PMR pain, family med pain, psych pain so the starting base salaries for anesthesia pain in these areas were far lower than I expected. In addition, gaining referrals was a huge problem in the metro cities. If you want to make more than your anesthesia colleagues most likely you will need to sell your soul to either the surgeon, lawyer, or narcotic seeker. I called surrounding spine surgeons who told me if they want their referrals then I should recommend spinal surgery if the first epidural is not a home run. I also heard many horror stories of poaching staff, patient, and difficulties of starting a practice with lower reimbursements. In addition, difficulties of acquiring ownership at an ASC.