Just as the quality of your undergraduate University affects the competitiveness of your Medical School application, the quality of your medical school affects the competitiveness of your residency application. However, ultimately your board scores certainly have a higher weight in the ranking process. After all a 240 from Harvard is the same as a 240 from the worst medical school in the country. You would still be considered a superior applicant with the knowledge you need to excell in any program. However all else being equal who do you think that the selection committee will give the nod to. I know that Stanford ranks your medical school as part of its scoring of applicants for anesthesia residency positions.
Have you read
http://forums.studentdoctor.net/showthread.php?t=478388 ?
Regarding post residency competitiveness for jobs, if you are certain that you want to live in a particular area of the country you would probably increase your likelyhood of finding a job there by attending the best residency program that you could in the region, unless you can match at an elite program with national name recognition. Why? Because your future employers/partners will be personally familiar with graduates of your residency program, if not graduates themselves.
But don't listen to me, I apparently am a D-Bag, doubly so?

Regards.