Hi Krishan,
Web AppBuilder for ArcGIS should be able to work with both WFS and WMS services.
In the case of WFS services, they will behave as they do in the ArcGIS Online map viewer. For some details, see this blog: What’s New with OGC Support in ArcGIS Online (June 2016) | ArcGIS Blog
I just tested a WFS service in Web AppBuilder and the content displays, pop-ups are supported, but you're right - the Analysis widget does not seem to be working with its content. We are investigating this issue. Can you please contact Esri Tech Support so we can get additional use cases to test?
For WMS services, you can add them to Web AppBuilder with the Add Data widget,
Add Data widget—Web AppBuilder for ArcGIS | ArcGIS
Hope this helps,