It’s not clear to me that “Columbia may be better” than Cornell if one is looking to go on to a doctorate in the field…
Notwithstanding how she interpreted the SEAS professor’s comments. What is IMO more likely the case is that SEAS is better at grad preparation than SEAS is in preparation for practice. Not necessarily better than Cornell.
Just because Cornell is effective at education for engineering practice does not mean it is ineffective for the purpose of attaining a PhD.
The available data suggests quite the opposite… Actually Cornell is consistently a top -five undergraduate origin of science & engineering PhD awardees…
Columbia produces fewer. On both an absolute and percentage basis.
See table 2 here:
https://www.nsf.gov/statistics/infbrief/nsf13323/
also see these old CC threads:
http://talk.collegeconfidential.com/college-search-selection/561639-top-producers-of-phds-in-engineering-p1.html
(note: Cornell % is distorted here- too low- since department had expanded in size, which was not taken into account).
http://talk.collegeconfidential.com/college-search-selection/559039-top-producers-of-phds-in-physical-sciences-comp-sci-math-p1.html
When I attended, the majority of engineering grads wanted to practice, but there were definitely people who headed for grad school- and good ones. These people got what they needed to accomplish that goal. But I don’t know how they went about getting there, so I can’t really help you with that… They probably needed to be proactive. And show obvious talent.
You might want to go to the department head, detail your objectives and try to get an advisor who will better help you to get there.