Believe it or not, up until only a year or two ago, we used to occasionally fly raw data VOR approaches on our Boeing 757s...despite them being perfectly capable of flying the approach much more accurately by flying the approach with reference to the FMC position (primarily based on GPS if fitted) since they left the factory back in the 80s!
It was a certification issue which meant we weren't technically allowed to use the onboard technology to it's full extent.
Now we are fully approved for 'managed' approaches (i.e. approaches flown from an approach loaded in the FMC) - either purely GPS-based or an overlay of an existing VOR/NDB approach. The raw data from the navaid is still dislayed during the approach as a cross-check.
Some of our 757s still don't have GPS installed and sometimes suffer significant map shift so we occasionally revert to flying the raw data VOR/NDB approach.
Large UK charter airline.
B&S