The FAQ has some great opinions on this topic. By own, evolving rationale:
Tip-Top Programs: The programs excel in terms of research, clinical experience, and teaching. There is also the "reputation" factor, but I like even more a comment from the FAQ: environment. In a tip-top program, the whole darn place should be an academic powerhouse. Anessthesiology interacts with most of the other departments in a hospital. Thus, those other departments must also be tip-top programs to support and foster and environment for excellence in anesthesiology.
Second-tier: These are the programs that have everything above...almost. I would say slight variations in the reputation or environment force reconsideration of these places as top-tier. This is unfortunate, since I wonder if the reputation and environment could come at the cost of, well, working conditions. The implication is that as far as a resident is concerned, a second-tier program in my book will still offer some of the best training and professional development available.
Third-tier: These programs are known for having excellent anesthesiology programs in solid academic hospitals known nationally. In addition to not having the reputation or environment found with top-tier, they may have areas where the surgery division is not super-stellar. Residents still get a mind-boggling strong experience in even the weaker divisions. Research efforts may simply be "younger" as well.
And finally, top-tier may simply be a personal feeling. Like big names and reputation? Harvard, Hopkins, Duke, UCSF seem the way to go. Like northern programs with mind-blowing experience, but a little "stealtheir" than Big Red? Perhaps Pitt. Want to stay away from "in the trenches" anesthesia training? A smaller program with a shorter work day, then.
In the end, I think it's all up to you.