Holding shift only speeds up the
visible movement of units. (and not by much)
Civ2 Earth map, 16 civs, Industrial Age takes about 30 seconds before it's my turn if there are not battles, and 10 more seconds before I can play, which is much better than Civ2/CTP2.
I think the time between turns is ok, not bad but not great either...
I wish there was some kind of "don't show enemy moves" option like in CTP2 though, because most of those 30 seconds was just the enemy visibly moving its units. And something to speed up the battles would be nice, because they take alot of time (especially if your unit becomes veteran/elite)