From my perspective following are differences:
1. If connection string is in
<connectionstring></connectionstring>
, it allows you to configure these from IIS-> Application properties -> Connection string tab. Isolates from appsettings.
2. If you are using any framework, then it would always read the connection string from
<connectionstring></connectionstring>
.
3. New tag allows you to encrypt just the connection string otherwise you will end up with whole appsettings encrypted and modifying appsettings would become tricky.
IMO always use
<connectionstring></connectionstring>
to store connection string.
-Rohit