First, that 25k "extra" is the fees you are paying for the extra semester worth of courses. You would pay the same if you do an extra semester in Gatech.
Second, Gatech "computational" expertise is a sales gimmick. At the end of the day YOU have to go and do leetcode/kaggle/hackerrank. The program will never teach you programming, just demand that you know it.
You last 3 queries may be answered reading through below
I have talked to my undergrad college seniors who have studied at either university.
As per 2019 Gatech QCF graduate (3.89 GPA), Gatech teaching quality in core FE courses was not at all good. You are taught by Industrial Engineering profs. who don't even try to relate to the field (Finance) and it is left to your imagination. Moreover, at that time the program had 0 industry professionals.
NYU MFE on the other hand is majorly taught by industry practitioners. The classes are extremely relevant to any field you are targeting and makes your interview prep. slightly easier, due to "related" content. The location advantage though not apparent now will soon be. In my experience (3 years in IB) finance hiring managers prefer face to face interviews as opposed to the remote interview trend in the Tech domain.
Furthermore, after with the population is "vaccinated" to covid-19 due to the mild Omicron varient spreading widely points to more in-person interviews by the time you reach that stage late next year.
Unless you are targeting the Gatech CSE specifically and are NOT especially interested in Finance or Financial engineering... You should choose the QCF, otherwise NYU MFE is clearly the better choice, both by quantnet/risknet rankings and my experience talking to alums.