Here are is my personal pro/con lists for medical. Full disclosure, I'm most interested in medical outpatient rehab, but a lot of this is based off of experiences in acute care. If I didn't do medical, I would want to work in a private clinic, but not a school (a little bit about that below). Sorry for the novel, I hope it helps!
Many different types of settings: acute care (hospital), outpatient rehab, skilled nursing facilities, pediatric hospitals, etc.
Fast pace and on your feet: I've shadowed an acute care SLP, and as a restless person I love running all over the hospital to get to patients' rooms, talk to nurses, etc.
Working with patients with acquired neurogenic disorders.
Getting to conduct and analyze VFSS barium studies with a radiologist.
Short prep time (for acute) and little/no standardized assessment: Unlike a school or outpatient setting, most patients will only be seen by the SLP once or twice, so things like a long standardized language test (which can be tedious to administer) aren't usually used. Assessment/treatment focuses on the most important things.
Dysphagia: I wasn't all that interested in dysphagia before shadowing, but it's actually really exciting because it's so important for the patient's care. You're actually making a difference in helping keep this person safe. And again VFSS are fun!
Counseling: If you really enjoy the counseling component, you will get ample opportunity for that with both patients and families (often in the midst of really intense situations). And on top of that it's been my experience that the other hospital professionals are a touch burnt out and because of SLP's/ASHA's emphasis on counseling, the SLP is often the brightest part of the day for these patients.
Making a difference: Like the above, you may be a real light to patients. I once watched a man writhing in pain start singing because he found the SLPs oral care with the toothette so soothing. Had to stop myself from tearing up.
Independence: It's probably true of most settings, but where I volunteer, the SLPs divvy up the patients on there own and spend as much or little time as needed with each patient.
You appreciate what you have: I know this is weird, but working with people who are sick and usually 70+ makes you appreciate your youth and health and has inspired me to try to live life to the fullest and to eat healthier. It has also made me want to cherish the time I have with my older family members while they're still healthy.
Potentially higher salary: generally medical SLPs are paid more (school SLPs have the opportunity for higher pay in areas with higher demand - definitely not a firm rule that medical SLPs make more, but common).
Job security: As baby boomers continue to age, SLPs will be in higher and higher demand and there won't be enough. (Let's get some more qualified applicants into grad schools!!!)
Oral care: Oral care is so important because the bacteria in the mouth could eventually make its way into the lungs should the patient aspirate. Ideally this would be something the nursing staff manages, but that's often not the case. The other day an SLP showed me a picture of a mass of food she had pulled off a patient's hard palate. Sometimes patients have like a white crust or some other residue that the SLP works on with toothettes.
Dysphagia: It's a pro, but also a con if you have a somewhat weak stomach. The other day a patient started hacking and the SLP took ample time examining the phlegm she coughed up. Sometimes there's anterior spillage, pocketing, etc. You do grow more accustomed to it, but things still get me sometimes.
Playing off the last point, speech/language makes up a very small part of the job if in acute care. Cognition is a little more prevalent, but dysphagia is the big thing you will do because keeping the patients safe is the highest priority. Also, the patients are often in no place to begin working on language/speech. That being said in an outpatient setting, you would probably work much more on speech/language than dysphagia.
Charting: Just like any SLP job, there is a lot of charting and often more time is spent on that than with patients.
Life or death: If you're working primarily with dysphagia, it's so important you're present and thorough in assessment and charting since your patients' health/lives and your own liability are on the line.
Working with families/doctors/nurses: Families are at an understandable low point and the SLP can be an easy target to receive their frustrations. Nurses do important work, but can also seem a bit burnt out and sometimes that can be felt. Though I haven't seen this where I volunteer, I've heard sometimes doctors can be really disrespectful to all other staff, including SLPs.
Sometimes it's heartbreaking: Sometimes the intensity is what makes it so great, and sometimes it's just hard to see. For me, these moments have been with terminal cancer patients and their adult children.
Not sure if this is a con, but if you're not in a pediatric setting, patients are usually geriatric, and you'll start referring to the 60-year-old as the "young guy." The youngest patient I've seen was in her late 40's.
A little bit on schools: I didn't want to say much on schools, because I'm not passionate about working in one so you should hear from someone who is. However, my biggest turnoffs from working in schools are the overloaded case loads, IEP meetings, and working with parents. At least in the area I'm in, SLPs have massive case loads and much of the treatment is done by SLPAs (woot woot!), with SLPs doing a lot of assessment and documentation. (I have heard private schools can be less hectic). Parents are passionate about protecting and getting the best for their child, and sometimes that can be intense. That's completely understandable, but I don't think I have the right skill set to enjoy working with them on a regular basis (the same reason I never wanted to be a teacher!).