For PhD, prestigious fellowship at university with poor infrastructure, or prestigious university? Two PhD positions were offered to me:


EPFL in Lausanne (Switzerland) 
In Italy, through a H2020 Marie Skłodowska-Curie fellowship.


I know that Marie Curie are quite prestigious, but also EPFL is ranked among the top 15 universities in the world.
I like both projects and both offer good scholarships. Although the cost of living in Switzerland is much higher than in Italy, the infrastructure in Italy is really old and scarce. 
I'm afraid of choosing the MSC ITN, which is at a university not as prestigious as EPFL.

To what extent does the prestige of a fellowship vs. the prestige of an institution matter to a researcher or professor career ? Is infrastructure a limiting factor for graduate studies in chemical and materials engineering?

"Poor infrastructure" means old equipment, not so nice labs, lecture rooms and PhD students offices. Also may you have to wait long for use an equipment... 
The infrastructure (roads, trains...) of Italy is good, not so good as Switzerland but acceptable.
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?