Turbofans
Turbofans belong in this discussion, especially as the vast majority (if not all) of current civil jet transports are powered by turbofans.
Here the jet core exists primarily to power the fan which supplies the majority of the thrust; so we find ourselves moving back towards the propeller case where a large mass of air is accelerated a small amount compared to the jet core.
How this all works out against altitude I shall have to leave to the more erudite. My guess is that the engine designers have optimised overall cruise SFC by balancing fan parameters against jet core parameters. And as others have mentioned, TAS gains at altitude are quite useful.
Now who can offer an explanation for why turbojets are more effective in the takeoff case than turbofans -- or at least were when compared against early turbofans?