Credit unions are a great place for senior citzens to have an account. Credit unions are not for profit institutions and do not have to pay taxes which gives them the ability to offer competitive interest rates. They also do not have hidden penalties or fees that most banks have which is a big money saver.
Also most credit union accounts are insured up to $250,000 by the National Credit Union Administration (NCUA) which is something for people to consider as an extra layer of financial protection.
In the long run it comes down to where you are comfortable banking and the amenities that your bank offers, but because of the not for profit structure of a credit union it is a great place to bank if you are on a fixed income or just want to save money.