Fabcloset, it really depends on the stone, but generally speaking, old cuts are a little less expensive than new cuts (this has always boggled my mind - they are so much more rare!). The recent trend towards antique diamonds has brought prices up from where they were 5 years ago, but most old cuts remaining in circulation will be in the lower colors (high colors carry a steep premium due to rarity, since many high colored antique diamonds were re-cut as cutting technology changed).
There is a dealer in NY who is now cutting new "old cuts" optimized to perfect proportions and light performance, blah, blah, blah - I personally can't stand them, lol, (why buy a copy when you can have an original? They all look identical and have no personality, but many people love them.) He is even specifically cutting them in low colors because these cuts are just particularly beautiful in the lower color range. My point is that the old cutting style is again considered beautiful and desireable, so prices are on the rise.
An Old European, for example, with excellent make (symmetry, polish, light play, contrast zones, general visual beauty), will be priced comparable to its modern counterpart. With old cut pricing, make is everything!
The main difference between the old and new cutting styles is that old cuts have generally chunkier/blockier faceting, more fire due to the delicious depth of the stones (I find it very visually rewarding to look at my diamond from the side and see that tall crown, small table - it's such a treat for the wearer - like wearing a ring pop!) They were cut for low light conditions, so seeing an old cut in candlelight, on an elevator, under a tree on a sunny day - will knock your socks off!