Hello,

You could find detailed documentation regarding the WebDropDown at:
http://help.infragistics.com/doc/ASPNET/2014.1/CLR4.0/?page=Web_WebDropDown.html

And using the control at:
http://help.infragistics.com/doc/ASPNET/2014.1/CLR4.0/?page=WebDropDown_Using_WebDropDown.html 

Reference to the WebCombo Class Members:
DisplayValue - The text content string of the top portion of the WebCombo.  
DataSource - Gets or sets the data source that populates the grid with data.  
SelectedIndex - Returns or sets the index of the currently selected Row in the drop-down. 

Reference to the WebDropDown Class Members:
CurrentValue - Returns/sets the value of the Value display dropdown component;if it is null the empty string will be used
Items - The collection of DropDownItems in the WebDropDown.  
SelectedItemIndex  - Returns/sets the selected item index in the dropdown item list 
SelectedItems - Returns the current list of selected items (applies when multiple selection is enabled)  
Items - The collection of DropDownItems in the WebDropDown.  

What is more, these are located under Infragistics.Web.UI.ListControls.
You could compare the name spaces too: Infragistics.Web.UI Namespace (WebDropDown)
In general, when you insert a WebDropDown into your project via the designer mode, Infragistics.Web.UI.ListControls will be automatically referenced. 

Since the Aikido Controls have completely different architecture than the classic one, WebDropDown should be considered not an upgrade to the WebCombo, but a completely different control. WebDropDown displays one column from your data model by default, however, you can show multi-columns in the drop-down container by using the template feature along with WebDataGrid as the control placed within the template.
http://help.infragistics.com/Help/Doc/ASPNET/2014.1/CLR4.0/html/WebDropDown_Create_a_Multi_Column_WebDropDown_using_Templates.html 

Probably the easiest and fastest approach, when in need to find a property or a functionality equivalent between controls, is to open the online documentation for the both controls and compare the APIs. As the new Aikido based controls are completely different, the knowledge of the classic ones could not be sufficient. This is why we recommend our customers (migrating to Aikido) to initially invest time and get familiar with the functionality via the online documentation and the online sample.
The online samples could be found at: http://es.infragistics.com/samples/aspnet/. Please notice, the header navigation section contains the controls, and the samples are accessible trough there.