The differences between ABAP classic and new debuggers are as below.
The classic ABAP Debugger runs in the same roll area of the main application. It is displayed in the same window of the main program. The new debugger will be executed in its own external window.
User can configure the interface of new debugger as required. New debugger has more than eight desktops and up to four different tools can be displayed at any point of time. This functionality is not possible in classic debugger.
Program called directly from the ABAP kernel cannot be analyzed with the Classic Debugger. Some programs like conversion exits can only be analyzed in new ABAP debugger.
Advanced techniques like Debugger scripting, External debugging, layer aware debugging are only available in new ABAP debugger.
You can set a watch point for an internal table only in new ABAP debugger. With this you can stop the execution of the program when an internal record count reaches certain value.
You can change debugger step size only in new ABAP debugger. With this you can step through each sub conditions separately inside a complex IF condition.