i think again, its going to boil down to whats personally best for you
you might want to have some savings separate from your main checking or another savings at a traditional bank. Like maybe having a savings at a local credit union b/c you probably wont touch it in case of a break glass emergency. Out of sight, out of mind. And a bank should be something that is located in most of the places you frequent to avoid crazy ATM fees and shit while traveling, assuming you want to use cash in the first place.
you dont use these institutions to get rich b/c you talking about what...maybe a percent of interest earned for using them. That's going to go for both of them. BUT, having some money stashed at a credit union and a history of the account might be looked upon favorably in the event you decide to take out a loan.
I think the most important thing is having a good credit score and that should be the focus b/c no matter where your money is, they gonna look at that before determining how much they are going to loan you
hope this helps