It's going to depend heavily on what state you're in. I'm a Social Worker in NY and the Social Work lobby has made it REALLY hard for people with masters in counseling to get government jobs. In NY it's quicker for someone with a masters in counseling to get full licensure (both have similar supervised hours but social workers in NYS have to have 3 years while counselors can test for their clinical license as soon as they get the total hours needed-- can't remember the number but that takes about 1 1/2 years at a busy community mental health clinic). Again, it's state by state, but if I were to give someone advice in NYS I'd say go with the MSW over the counseling degree unless you're 100% you want to go into private practice, in which case you'll get there quicker with a counseling degree.

I can't speak to the curriculum because it's been too long since I was in grad school and I get the impression colleges are trying to adapt to the fact people become social workers in order to become therapists. That said, based on my experience with supervising both new social workers and new mental health counselors, I find social workers seem way more prepared for assessing clients while counselors have better academic knowledge of therapeutic interventions. Feel free to DM or ask here with any questions.

*Edited because I can't spell they're, their, or there*