I have direct-transferred from TIAA-CREF to Vanguard a few times, and have one transfer pending now. In the past, I was pleased with both sides. T-C mailed out checks immediately the day after my phone call, charged no fees, sent me confirmation with the check numbers, and Vanguard got the check within four or five business days.
With my currently pending transfer, T-C mailed out the check a month ago, and Vanguard still has not invested it, though I find it hard to believe that they have not received it.
Some things to consider:
I wouldn't recommend transferring just because Vanguard has a wider selection of options. They have to be options that you need. There isn't anything at Vanguard quite like the TIAA Traditional Annuity or the TIAA Real Estate Account (maybe with good reason in the latter case!)
It's possible to consolidate to a TIAA-CREF IRA too, which may have more investment options than the plan(s) you have now.
Fees at Vanguard are lower, but only by a few basis points. It's not as if you're transferring from Merrill Lynch or AXA Equitable!
You might consider transferring assets in-kind, if you're worried about being out of the market. Not sure if Vanguard would accept this.