Main difference between classic ado and ado.net is as follows

ADO 

Classic ADO have recordset

Its objects communicate in binary mode

ADO supports mostly connection oriented models

Since ADO derives information about data implicitly at run time based on metadata, it is an expensive process.

Only Client Side Cursors are allowed in ADO classic.

ADO.Net 

ADO.Net have Data Adapter and Data set

ADO.NET uses XML for passing the data

ADO.Net works in Disconnected manner

By leveraging known meta data at design time, ADO.Net provide better runtime performance and more consistent runtime behaviour

ADO.Net Support both client side and server side cursors