From the small bit I know about non-medical graduate admissions, the rigor of the program is a factor in graduate admissions but it only matters when comparing a candidate with good grades from a weak program and a candidate with equally good grades from a strong program. Again, it's all about the student and how well they can prove they learned the material, not about prestige.

If you really want a more in-depth answer to your question, go to https://academia.stackexchange.com/ and see what practicing academics say; this sort of question has surely been asked and answered many times. (I'd dig up some links for you but, not to be unkind, the very first thing you'd better get used to if you hope to reach graduate school is finding stuff out on your own given some hints.)