Hi! I can give you our experiences!
We've bought and sold flats in period buildings (primarily Georgian) for about 10 years, we've done them up, lived in and then sold when the time was right. We did this because we wanted to live in a particular area we love but couldn't afford the houses.
We fell into it by coincidence because we moved to the area from somewhere else and it's worked out amazingly for us, I'll write my positives and negatives, but for us the positives have far outweighed the negatives.
Positives:
-a more secure investment, we've never lost money on one, infect we've made significant amounts each time: £180,000 profit on first place (over 4 years though) £102,000 on second (over only 10 months) £70,000 on third over a year, £100,000 on the place we've just over over 2 years. We have friends and family that have lost significant amounts on new builds. Of course you need to buy the "right" property, needs work, sought after area, etc etc.
-tend to be more sort after (husband now works in property)
-beautiful!
-older buildings tend to keep cooler in the summer
NEGATIVES:
-need work and maintenance
-other people who live in the building, can be fine but you don't always know what you're getting!
-cold in winter, high heating costs!
-be careful of damp if on a ground floor