I am a prospective PhD math student. This year's application season has brought me down to two schools to choose from:
Medium-sized department, ranked <80 on US News (whatever that means), very welcoming people, potential advisor is very young but seemed like we would "click", surrounding area and city is beautiful, program looks awesome.
Larger department, top 20 program, potential advisor is famous in his field, current advisor says I would work well with him/he's a cool guy, don't know much else since I've not visited.
I am waitlisted at university 2. University 1's initial offer to me included the standard stipend along with a decent fellowship. I made a visit to university 1 and talked with many professors and my potential advisor. After this visit, they offered me a ~17% increase in my stipend due to some professors advocating for me who were apparently impressed (whom I do not know other than my visit). I feel that this is a good sign, but I am ultimately pursuing a career in academia. So I know prestige plays a big roll in future jobs. Assuming I have an offer from university 2 as well:
Is this late stipend increase offer typical?
Based on your experience and insight in the job market for academics, which university is the better option?
Thanks for your time to read.