How much better are aerodynamics between a vintage road bike and a top of the line aerobike?
The bike's proportion of total air drag is roughly 20% (for a road bike, more for a TT bike as the rider assumes a more aero position), with the rider accounting for the balance. 

So assuming exactly the same bike fit and rider position, then even if the new bike halved the drag coefficient of the old bike, it would mean a drop of only ~10% in your total coefficient of drag.

A 10% reduction in CdA, while a decent improvement, would result in ~ 3.4% increase in speed on flat terrain.

So a bike with 50% the drag coefficient of another results in ~ 3.4% speed gain. 

If the aero differences of the bikes are less, then of course the potential speed differences will be quite small. What is significant of course depends on how much a given speed gain matters to you. 

And just to set an upper limit to speed gain from changing bikes (same bike position), if the bike had zero drag (impossible of course) then you'll still only attain a ~ 7-8% increase in speed. That's the approximate theoretical upper limit.

If the new bike fit is aerodynamically worse than on your current bike then you may even go slower!

So while a nice aero road bike, assuming same bike position, will result in some speed gain, the bigger bang for buck is attaining a more aerodynamic position on the bike. As others have commented, this is often done with the use of aerobars fitted to the front of the bike to enable the rider to attain a much more aerodynamic bike position.

Of course you can do both and have fun trying!