ADO.Net is an acronym for Advanced Data Objects, basically Ado is a database connector, which uses SqlConnection/OleDbConnection for database connectivity, it is difficult to debug but easy to understand and maintain. it used the T-SQL to query the database. Accessing SQL based databases using ADO.Net is fast and efficient. However, data is often returned as different types or custom types, and have to be cast or formatted into usable or .Net or native types.
whereas LINQ, is a part of .NET Framework since .NET Framework 3.5, Easy to debug and cause syntax errors at compile-time. It has full type checking at compile-time and IntelliSense support in Visual Studio, since it used the .NET Framework languages like C# and VB. it is popular cause it allows you to stay in your native programming language (C# in this instance) and query data, or any other collection of objects for that matter.
Editor, DotNetSpider MVM
Microsoft MVP 2014 [ASP.NET/IIS]