It is not as easy as just pitting ancient against medieval in terms of cost efficiency. There is way too much variation in each of these broad fields. For example, If I wanted to collect budget coins of the Roman Empire I would focus on the 3rd and 4th centuries. There are plenty of affordable coins in these centuries. However, I would not focus on the first century CE. This is the rea of the 12 Caesars. These coins are sought after and can be very expensive. To some degree this depends on the meal you collect. Bronze coins will generally be cheaper than silver, and silver will generally be cheaper than gold. Notice I say generally as there are exceptions to this. Some rare sestertii of the Julio-Clauian will cost thousands. Some rare silver coins will be more expensive than gold coins.
The same sort of thinking also applies to medieval coins. If you collect medieval coins of Hungary there are plenty of affordable coins. However, if ti is British hammered you are looking for the prices will be much higher. British hammered gold can also cost several multiples of other European hammered gold. French medieval coins are available and many are affordable, but certain types are very attractive to some collectors and the prices will be much higher. In my experience many feudal coins are affordable while the royal coins are much more expensive. There are of course exceptions to this as well. Some coins are sought after for their connection to history. For example, coins of Eleanor of Aquitaine are not considered rare as regards the references on the subject. However, try finding one for sale. I waited well over to a year to find one that came to auction.
In short, it is all about what are of collecting interests you most and what your budget is. There is no single division between ancient and medieval which in my opinion would make one area more attractive than the other as far as budget issues are concerned.
The same sort of thinking also applies to medieval coins. If you collect medieval coins of Hungary there are plenty of affordable coins. However, if ti is British hammered you are looking for the prices will be much higher. British hammered gold can also cost several multiples of other European hammered gold. French medieval coins are available and many are affordable, but certain types are very attractive to some collectors and the prices will be much higher. In my experience many feudal coins are affordable while the royal coins are much more expensive. There are of course exceptions to this as well. Some coins are sought after for their connection to history. For example, coins of Eleanor of Aquitaine are not considered rare as regards the references on the subject. However, try finding one for sale. I waited well over to a year to find one that came to auction.
In short, it is all about what are of collecting interests you most and what your budget is. There is no single division between ancient and medieval which in my opinion would make one area more attractive than the other as far as budget issues are concerned.
"Cave ab homine unius libri"