For PhD, prestigious fellowship at university with poor infrastructure, or prestigious university?
As astronat says, the prestige of the university matters very little when you do a PhD. However, the prestige of the fellowship that funds you matters even less. Divorce yourself from the notion that these are the important metrics to evaluate, and instead look at:


Which advisor will you work with, and what are their students doing now?
If you have a chance to talk to PhD students at both institutions, do so.
Which university/grant will offer you better conditions, such as salary (of course after taxes and costs of living) or teaching load?
Which city would you rather live in for the next 5-ish years?
And, last but not least, which of the options makes you more excited, personally?