MSE walls have been in existence since the 1960's. The backfill in the strap zone is a select fill that drains well. They are built all over the world and in pretty much every intersection built today. You probably don't even notice them. Extensive studies have been completed by almost every testing organization there is out there.
Today, they even use geosynthetics for straps, but they are more difficult to place.
Do you really want to know cost differences? LOL. Because I'm a civil engineer and estimator. It's what I do for a living.