Really, counseling programs (leading to LPC) and MSW programs lead to a lot of the same career trajectories for most people. I received a MSSW (same as MSW), and I've worked in many of the exact same positions as counseling MAs. However, there are some differences that you may want to keep in mind. I do want to warn you that my experiences/observations are limited to Texas and Louisiana.
First, most people get masters in counseling to become a master's level therapist as a LPC or LMFT or both. (Even if you eventually get PhD's in those fields, you will still be a master's level therapist and be reimbursed by insurance companies as such). Some schools allow students to take the prerequisite courses to pursue both licenses simultaneously, and others want you to pick a track or a separate program (like clinical mental health counseling versus marriage and family therapy). It varies among institutions and also between states. But anyway, my point is this: just like the MSW, you have to apply for a provisional license after you graduate from school. They are called different things in different states, but examples are the Provisional Licensed Professional Counseling (PLPC) or the LMFT-Associate (LMFTA). In order to attain full licensure (LPC/LMFT), you have to pay for and undergo clinical supervision and then pass a test to practice independently and to sign off on various psychosociall assessments which are required to be performed by a person with a full license So, you can't just stay provisionally licensed. You are expected to become fully licensed.
With the MSW, the process towards clinical licensure is very much the same. However, the end game for someone with a MSW isn't necessarily to become clinically licensed. There are some people who go into social work school without intentions of ever becoming therapists. It's considered totally fine never to get licensed beyond the LMSW. A lot of these people find a niche in medical social work, sometimes administrative/policy type jobs , and other types of case manager or even supervisory positions. Of all these types of jobs, I believe that the only one that is exclusively the domain of the LMSW is medical social work. (Correct me if I'm wrong). With the other types of positions, you can have a variety of bachelor's and/or master's degrees. It just kind of depends on your work experience and to what degree you are able to prove yourself. As far as casework - unless you live in an expensive, competitive city, you can get a case manager position with almost any type of bachelor's degree. So even though there are LMSWs who work in this capacity long term, I would not recommend going to social work school only to pursue this path. If you're hoping to move into management, a master's degree may help, but it isn't always necessary. It kind of depends on the exact industry/agency that you're looking into & a MSW may not be your only or even best option. If it's a clinical managerial position, a master's in counseling or MSW are usually considered equally qualified.
This being said, most people who get MSWs do pursue the LCSW because that is where the best and most plentiful career opportunities are.
Another important thing to remember is that, like someone mentioned, only LCSWs can bill Medicare. This is very much about the effectiveness of the social work lobby than anything regarding the superiority the degree/license. LPCs have been trying to get that privilege for a while now, but I don't know when and if that will change. So in some instances, LCSWs are preferred for this reason. It may or may not be a big deal depending on what kind of jobs you want to pursue. I get the impression that the Veteran's Administration prefers LCSWs - maybe for this reason? Not sure...So, even though it's not fair & should change, LPCs are still able to find work and I don't know any that are starving to death due to this obstacle.
One thing about schooling; if you KNOW that you want to become a therapist and not.. a medical social worker, for instance, you might appreciate that in the curriculum itself, counseling master's will teach you more clinical skills in your coursework. MSW programs definitely cover clinical topics (and this also varies among schools & different concentrations within the schools),but usually not as much so. I feel like you do eventually learn everything you need to learn when it's all said and done, but I learned a lot through supervision and work experience. Also, know that some (NOT ALL) clinical mental health master's programs are moving towards the three-year model, while most MSW programs are two years full time.
At the end of the day, they are pretty close, and none of these degrees are ones that you want to pay a lot for. Prestige of the university for any of these licenses REALLY doesn't matter, unlike some other fields. The pay is often crap, especially when you first get out of school, though you can eventually make a decent living. Your decision may actually just come down to COST and convenience. Which programs are around you? Can you do any online? Do some have evening/weekend classes? Which offer the best PRICE? So if it's a MSW from Columbia versus a MA from a CUNY school, trust me when I tell you you're going to want to pick the CUNY master's.
Hope this helps!