MGH/McLean is generally considered one off the top 5 training programs with one of the top 5 faculties. Serious academics would disagree over its placement within the top 5. Outside of Boston and outside of its alumni, I don't think academic psychiatrists see it as clearly better than the other elite places. In other words, if you are just looking at rep, you are just as likely to get the opportunity to get to the next level (eg, a top-notch research-oriented fellowship) from any of several places. If you ask your non-medically-oriented cousin, however, he or she will be far more impressed by your having trained at Harvard than, say, at UCSF, because your cousin will never have heard of UCSF even though it is one of the great medical meccas of the world. If you want to impress your cousin and can get into MGH, have at it.
In general, however, YOU (and your talent, motivation, effort) are much more important than your specific training program. And you + mentor can be the biggest single factor, and the big name places tend to have big names because they tend to have lots and lots of well-connected, productive teachers who can not only be role models but can help get you a job. But it's not clear cut.
For example, MGH has more big name academic psychiatrists and is more difficult to get into than Longwood, but, IMHO, if you go to Longwood and get successfully mentored by--for example--its chair, who is a neuroimaging expert, you are much more likely to get a top-notch research fellowship than if you are a solid generalist MGH resident. This is true not just because you will know more but because Dr. Silbersweig has neuroimaging street cred and will push/ensure your acceptance at his or another program. A similar comparison can be made in New York between Columbia/Cornell [which are probably the 2 most difficult programs to get into in the city and probably have the biggest elite faculties] and NYU/Sinai/Einstein/St. Vincent's, etc which are very strong in lots of areas and are a better choice for certain types of residents. IMHO, a similar situation is also seen in Northern California, where UCSF and Stanford are more famous but UC Davis may be at least as likely to propel certain residents into academic careers because of comfort/fit, etc.
It is true that MGH/McLean and its peers have a higher number of researchers with international street cred, but it is also true that you may not connect up with an approachable mentor if you don't feel comfortable with the program. Further, if you and the program are a bad match, you may flail clinically and will likely be unable to take advantage of the research options that might be available only to those who are cruising with the basic material.
Anyway, while it's impossible to give a specific answer, and I do have a bias towards going to as rigorous a program as you can get into, I also think you should go to the place that feels like the best fit. You can create your career as you go along.
Oh, and by the way, there's a BIG difference between being a department chair at a medical school and a PD; most of the former are serious, hard core researchers, and most of the latter are clinicians with relatively lightweight research. Occasionally, people go from training director to chair, but it's increasingly unusual because it calls for different skillsets and cv's.