TCEP is "stronger" than DTT which is in turn "stronger" than BME. Each agent has its own peculiar features:
TCEP is bad in combination with phosphate (it goes away) and is a fairly selecive reductant, In is HCl salt form, TCEP is hideously acidic (several molar equivalents of strong buffer or NaOH needed to neutralize it). On the other hand, it stores like a champ at pH 6.5 in 1M solution on bench top.
DTT and especially BME can form mixed disulfides with protein Cys, and have other reactivity features (e.g. they can interfere with derivative soaks esp. if present at high concentration)
BME gives Artem (and several people I know) wicked headaches, even at minimal exposure.
For TCEP I would recommend starting at 1mM, whereas for DTT and esp. BME I would recommend 10-15 mM and higher.
Artem
"certified BME-free lab"