I did residency at U of Chicago and fellowship at UCSF, so I might have some insight. At U of C, they don't typically have fellows, although they have for the last 2-3 years. They only take 1-2 per year, so you're not really engrained into the culture of the institution, which I think is a negative. The Pulm/CC fellowship has always been REALLY strong and the site of some noteworthy papers in critical care (a FACTT site, and the seminal paper in daily sedation interruption). I think that maybe overshadows the anesthesia fellowship. This might be somewhat different now that the IM dept is in a shambles (the chair, a prominent pulm guy stepped down in protest of hospital politics).
On the plus side, the anesthesiologist-intensivists are outstanding clinicians and educators, and I'm still in touch with and collaborating with several. The units are called closed, but no one is fooled; the cardiac and burn surgeons are very involved (and I would say in the case of the cardiac surgeons, engaged in active subterfuge; it's a drag. You'd be in the middle of rounds with the team, the surgeon would show up, and the gensurg resident would literally break off from the team and go huddle in the corner with the surgeon and make all the decisions). Anesthesia recently "took over" the general surgery unit, whatever that means. Sounds like it's going pretty well, although, again, I would hesitate to call it closed.
That said, if you want to be in Chicago, it's the only real fellowship. Northwestern has one, but as long back as I can remember, the experience was limited to neuro and trauma (not counting observational rotations through the other units).
UCSF is largely an open shop as well, with the exception of heme/onc and surgical subspecialty patients, which are closed (but again, it's not like the surgeon is just going to be hands-off; they're always involved and often overbearing). That said, you cover every type of patient except cardiac surgical.
I would say, in general, there are very few places (Columbia maybe, or Vanderbilt, so I've heard) where the anesthesiologists are truly left alone to take care of patients. It's just the reality that surgeons don't think anyone knows medicine or their patients as well as they do. Within that context, then, a good fellowship will give you broad exposure to lots of types of patients and the opportunities for autonomy in management and navigation of the often complex collaboration between services that defines our work.
In that regard, I think UCSF was an outstanding place to train. I'll have a better sense for that as I progress through my first year as an attending, which will be partly at UCSF in that open model, and partly in a closed medical unit.