First off, the structure of the wood itself would be different than a new factory instrument, due to ageing and playing for over 200 years. 

Second, the wood would have been hand selected. 

Third, the trees were different.  Same species as we have today, but wood from a violin made back then would have been from trees that grew during the "little ice age", which was a period of very cold winters and short summers.  That makes the rings of the trees closer together, resulting in a denser wood than we usually find in most places today.  Denser harder wood can be carved thinner and still be strong enough.

Fourth, they used different finishes back then than are mostly used today.  Especially different from modern factory finishes.

Fifth and probably the most important? (at least in my noob opinion).. Hand craftsmanship done by people who actually took great pride in their work and wanted to make something of excellent quality that would last.

Those are at least some of the reasons I am aware of.  The more experienced folks here probably can add to that list.  

To sum it up in just one line: 

"Because they just don't make them like that anymore.."