I have seen the difference between these small reputed places and large public schools with greater resources, and my impression is that the intellectual vibrancy and close knit departments in the Ivies etc. smaller programs kind of make up for their lack of breadth in resources.
Plus people say at the end one has to sell the PhD to become a post-doc and then brand value often matters.
My final message is to not rush to judgment based on US News and World Report or NRC rankings. There are many parameters that will affect your graduate experience, and reputation / pedigree effect is just one such parameters. Make sure you visit the campus and talk to faculty members and other students, go on lab tours - don't be shy, ask a lot of questions.
You need to find a perfect fit between you and the department (or more specifically, a lab or a PI that you want to work with). It's a bit like dating - physical attractiveness (ranking) is not everything - you need to find a "perfect match" in many other ways.
The other professor is right about not paying attention to ratings. I had a choice between a school that was then rated about 50th and a school that was top three (maybe top one). I chose the lower-rated school since I liked the location, the atmosphere and the friendliness of the department. It just fit better. Sure, it might have hurt a little bit in getting future jobs, but I was very happy for 5-6 years, and that made it worthwhile. It was the best decision I've ever made (and the higher rated school's admissions person was stunned....)
I think being from (any) ivy as an undergrad might help in getting into REU programs. From looking at old forum threads I've found that many ivy students who aren't at a tiptop physics program and have average grades/GRE scores have gone to 2 and sometimes 3 REUs.
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