Just wondering in terms of actual employment for psychiatrists, how important is the prestige/quality of the residency program that one attended?
Not at all. If you're a decent doctor, you'll get plenty of patients and job offers regardless of where you trained.
Also, I should point out that you say "prestige/quality" as if the terms are directly interrelated. I'd argue that one could get better "quality" training at a strong community hospital (St. Luke's-Roosevelt, Hennepin, etc.) than at some "brand name" programs (Harvard South Shore, and probably many others) or other academic programs (Rosalind Franklin, Drexel, etc.).
Do the graduates from the more elite psych-residency programs land better positions and command higher salaries?
As has already been pointed out, the general answer is "no" if you want to be a general outpatient psychiatrist.
If you want to go into academia, it does help, but I think that a large chunk of that is self-selection. The people who want to go into academia generally prefer to train at prestigious academic hospitals, so it's natural that the faculty at prestigious academic hospitals will come from prestigious academic training programs. Also, the prestigious ones will give you more research opportunities, which attracts more researchers, which opens more doors for academia.
Also, if you want to subspecialize, you'd probably have more doors open if you were able to do a lot of electives in your subspecialty of interest, which would be easier if you were at a big academic program. For instance, Cleveland Clinic isn't known for psych, but a lot of their psychiatrists are able to subspecialize in pain medicine and sleep medicine because they have a pathway for that... so in that regard, training at that program could help you make more money.
The same is also true for forensics, which may not be super-competitive as a whole, but is one of the few subspecialties in which brand name supposedly matters. This is based purely on anecdotal evidence, but I've heard that lawyers pay more for a forensic psychiatrist who trained at Yale.
What are the real benefits, if any, of having attended a top residency program as opposed to a decent/less regarded one?
1. Research/academia, if you're interested
2. Ego (which becomes #1 if you're not interested in research/academia)
3. Possible increase in fellowship choices, depending on the specific program
4 (or maybe 3). More exposure to "cutting edge" stuff, if that interests you. It's not a huge deal, but it'd be nice to have some exposure to TMS, VNS, DBS, etc.
5 (or maybe higher). Wide selection of psychotherapy supervisors, depending on where you go. If I were interested in psychotherapy, I would have begged for an interview at CHA and I would have ranked Baylor #1 of the places where I did interview. Again, this is probably not a huge deal, since most programs will allow you to do as much psychotherapy as you please.