I can answer specific questions about rheum if anyone has them.
Fellowship is great. Pretty chill most places. Clinic & hospital consults. Share call with co-fellows. I never once had to come in after hours for a consult, and usually would only get 2-4 on a whole call weekend at a large academic program (2 hospitals covered, combined ~1200 beds). Call for us was 1 in 6 weekends. On call, you might also get a few patient phone calls ("can I drink 10 beers while I'm on methotrexate?" "uhh.. no, thanks for calling" ... "I have a fever and I'm coughing up blood" "OK, go to the ER. The consult fellow will see you tomorrow"). No primary admissions, no ER consults.
I have just started my first "real" job, and it is almost entirely clinic patients, 8-5ish, call is 1 in 5 weekends, again mainly just patient calls and once in a blue moon a hospital consult that can't wait to be seen as an outpatient (most can, actually). Outside of academic centers, virtually no rheumatologists go to the hospital on a regular basis unless they are like me and trying to build up their practice. Infusions and IV treamtents are done in the office, and if patients need hospitalization for an infection, renal failure, etc, they go to a hospitalist who will just ask you what needs to be done over the phone.
The shortage of rheumatologists in most places is such that you can find a job pretty much anywhere except for the most major metro of major metro areas, and even then you can probably get a job if you sacrifice starting pay a bit. The other advantage of shortage is that if you don't want to see OA, fibro, and other assorted ouchies, you don't really have to. I choose to because a not insignificant number of those people will actually turn out to have RA, gout, SLE, etc that everyone else missed. Also, they are legion in number and are a good way to build your practice fast and get word of mouth referrals (assuming you are a good listener and nice to them).
Otherwise you get to see lots of really great, interesting stuff in rheum. Vasculitis, weird mononeuritis, multisystem inflammatory problems that nobody else can figure out. If you like puzzles, interesting cases, and an extremely wide diversity of pathologies, rheum is a great field for you. If you want to look at stool on a TV screen all day then drive home in your Maserati, it may not be for you. One of my attendings used to say "if you don't love a good gout case, you shouldn't be a rheumatologist" and that is true. I would also say if a patient with fever, weird lab results, a rash, and arthritis doesn't get you jazzed up, rheum may not be for you either. Rheumatology has also changed dramatically in the last 15 years with the introduction of biologics. The era of making a bunch of moolah off of infusions is pretty much over, but what remains is that we are actually able to make dramatic improvements in things like RA and vasculitis that just weren't possible a generation ago.