I got accepted to one of my top choice schools for a math Ph.D. However the graduate students there said in the past few years, the Ph.D.s before them (both pure and applied math) had quite a bit of trouble finding postdoc positions after graduating. But they are able to find nice jobs in industries.
Would this be a red flag? I know that finding a postdoc or a tenure track position in math is especially hard in the recent years, so this might not be a complete measure about their Ph.D. program.
I have also gotten accepted into another public university and the graduate students there said they didn't have much trouble finding postdocs. This one is not as prestige as the one above in term of general ranking.
I have professors that I would like to study with in both universities, and I am leaning toward the second one.
Could you give me some advice?
I'd recommend trying to gather some objective data on outcomes. For example, in the mathematics genealogy project you can search by "name of school" and "year of degree" to find a list of people who graduated in 2014 or 2015. It's not guaranteed to be complete, and it sometimes mixes together people who were in different departments at the same university, but it's usually pretty good (and sometimes easier than finding this information on math department websites).
Then you can start googling people, with "math" appended if necessary, to see what you can find. If you can't find any indication that someone is working in academia, then they probably aren't. If they are, then you can gauge how pleased you would be with such a job.
This should give more reliable data than self-reported difficulty of finding postdocs, because it avoid filtering through the departmental culture. Some cohorts of grad students are optimistic and enthusiastic, while others are more apprehensive, and it's not clear to me that this correlates particularly well with actual success on the job market.
It's also worth keeping in mind that the relevant issue is job opportunities, not actual outcomes. If one person complains about the difficulty of finding a job and another doesn't, you can't conclude anything without knowing where they were applying. (Sometimes students at more prestigious universities apply mainly to fancier postdocs, because they wouldn't be happy with less prestigious jobs.) Unfortunately, this is more difficult to gather objective data on, but I think it's a second-order effect.