My husband has TIAA-CREF and I rolled over qualified investments from previous employers to TIAA-CREF.
Questions like this are tough to answer, because I am not sure what your goals are, how actively you want to manage your investments, and so forth.
Here's our situation - we used to pay an advisor 1.25% (face punch) to "manage" our investments. I never saw the value.... after a few years we dumped him. It's the classic scenario: Even net of fees our advisor wasn't beating the benchmarks. That said, we wanted to consolidate things and exercise more discretion over our own funds. We looked at TIAA-CREF and at Vanguard and decided to stay with TIAA-CREF. Because we had over 500K in assets, we are able to use a no-fee advisor who sits down with us once a year and works on allocations, applies their econometric research, and generally helps us with paperwork when we are tired of trying to do everything online ourselves (sometimes I like a little extra service.) I like the fact that we have a "go to" person to grease the skids, and that TIAA CREF has brick and mortar location in the city where we hope to retire.
Not sure if Vanguard would be better, but all I can say is that TIAA-CREF has been very good and I'm not likely to overthink it. Vanguard and TIAA-CREF both have great reputations and a lot at stake... I don't see them ever taking risky positions or failing to serve the interests of their clients. I wouldn't worry about the minutiae. If you're saving at Mustachian levels and following a reasonable allocation/strategy, it will work out either way.
We also hold some non-qualified money in Vanguard, but it is small in comparison to our total portfolio.