To answer your second question - yes. But rotating through there, during your clinical years is a must, and that is how these programs recruit their candidates. Very few people decide to go into neurosurg each year. But it is still more than the # of available spots 🙁
-Renowned faculty
-Great teaching
-Caseloads for residents
-Research output
-Quality of residents they take in
-Quality of graduates they turn out
-Prestigious fellowships obtained by graduates
-Money pumped into the department/division (which goes a long way in updating facilities, supporting research, attracting/recruiting all-star faculty to the program, etc).
In terms of academic and clinical rep, I think the top programs are the following
Brigham, Columbia, Virginia, Barrow, Michigan, Mayo, Southern Cal, UCSF...these programs all have strong histories of producing top-flight academic surgeons, and going to one of these places WILL help you get a better job if you want to go into academics. For example: Columbia's two chiefs last year wound up becoming attendings at Hopkins and UCSF directly out of residency; one of USC's chiefs from last year also had a faculty appointment at Cal Tech; Virginia's Chiefs from 2003 are going into peds fellowships at Brigham and Toronto (two of the top peds programs)
IF your interest is private practice, most programs are pretty comparable. You'll here a lot about operative experience when you interview, but keep in mind that any program that is accredited will get adequate case volume. Go to the place where you fit in best.