Hi. What is your opinion on this matter?: Is it better to get Econ degree from one of the top schools such as Notre Dame, Vanderbilt, USC, Cornell or Finance degree from schools ranked 50 - 100 in US ranking? Which degree would be more helpful in the process of finding a finance-related job? Does the prestigious name of the school matters more than a degree itself?
Check the recruiting opportunities by school. If it is clear that the finance degree is a better feeder into top firms than those econ degrees, go for the finance.
Economics at top schools.
Finance degrees from business programs at schools outside the top 50 will have far fewer job possibilities than economics majors. In fact, finance majors may be passed over for finance positions by students from top universities/LACs with excellent grades in any major whatsoever as long as the student has sufficient math skills and internships. Williams’ Art History is kind of well-known for that 
but without going to that extreme, you have lots of examples (check out Hamilton, for example). Seek out Blossom and Taxguy, adults on this website who are higher-up people in charge of hiring for big-deal companies, and ask them straight up.
Don’t place so much on rankings. The prestige may help for contacts, but overall it doesn’t matter where you go as long as you apply yourself and get your name out there. There’s another thread that talks about how Economics is now a major for people who want to go into business but not major in business. If you want a finance-related job, then it makes the most sense to get a Finance Degree.
I forgot to mention that I am interested in working abroad (In Europe or Australia) some time after graduation. I assume that econ degree from prestigious university will hold more weight than finance degree from less known school? Is that true in general?
yes, if you want to work abroad, the name of your university (ie., state flagship, Ivy, etc) will be useful, UNLESS you attend a university with a history of strong placement in TNCs.
If you want to work in finance, you’re better off with a strong math/stats background than with strictly a finance major without a lot of extra math (many finance majors require calc1 + stats for business - you’ll want 2 classes above each.). A finance minor added to econ and/or math or stats is good of course.
Econ for sure. For Wall Street prestige matters A LOT. You can have an underwater basket weaving degree from an Ivy and you’ll still be more heavily recruited than one coming from a non target with a finance degree
^What @qpqpqp said. In most fields the prestige of your undergrad doesn’t matter much, but finance/banking is one of those fields where it does. The top schools have way more recruiters from top banking and finance firms coming to do on-campus interviewing and hand out internships and such. I’ve had students from Columbia and Barnard in all kinds of majors (psychology, philosophy, English, etc.) go onto banking and finance internships and jobs, not just the econ/financial engineering majors.
LOL I thought only my family used the term ‘underwater basket weaving’.
Didn’t know that you wanted to study abroad, OP. On that note, yes, go with the econ degree from the top university. As contradictory to my first post as that is, the name matters if you want to be that sorta Wall Street-esque business person and travel to China/wherever. The top schools will also give you more opportunity to pursue internships etc. with the big places.