There's not enough information to adequately answer your question.
What funds does each have?
TIAA-CREF has tons of funds and some employers' plans have access to more funds over others. My workplace uses TIAA-CREF and in 2006, they expanded our options.
You should be able to find out info about both and post that.
For Fidelity, look for Spartan funds. For TIAA-CREF, avoid all their access funds and most of the TIAA funds.
I personally use the TIAA-Traditional, CREF Equity Index, and CREF Bond Index.
I wish our company had Vanguard or Fidelity (with Spartan funds), or T. Rowe Price, but TIAA-CREF is a solid company and their are so many worse mutual funds out there.
This forum is consistently down on annuities, but TIAA-CREF's are the best (cheapest) and there are advantages to having an annuities. In William Bernstein's new book, Rational Expectations, he advises people to place their bare retirement needs into a TIPS ladder or a annuity based on how many investors failed to maintain asset allocation during the Great Recession and how many people he knew lost significant portions of their retirement right before retirement and made overall bad decisions.
Lots of investors on this forum talk a big game (it's easy to talk big when we've had an unrelenting bull market for 5ish years) of having 80% or 90% in equities even in their 50s or 60s, but when a massive correction comes, will they be able to rebalance and stick to it? Some (smart, cut off the emotional human side, or ballsy) will, but evidence shows many investors bail particularly when losses mount and the GFC with 40-60% drops caused that to occur with lots of people.
Good luck on your choice!