The biggest difference
in my eyes is
experience builder gives you a little bit more flexbility in terms of layout
allow you move bigger component such as panel component ( legend panel, layer panel ... etc ), map component around
In old web appbuilder, map component is fixed after you choose a layout template.
Now with experience builder, even after you choose a template, you still can resize or move around map component.
In old web appbuilder, layer component is not panel, it is a icon button, when you click it, it expand to a panel. When you click again, toggle it collapse the layer panel.
In new experience builder, old expandable toggle component still available, but added a new non-expandable, re-sizable, movable layer panel component.
The same thing happen on legend component.
These improvement give you a little bit freedom in terms of positioning layer, legend widget.
Widget and component is interchangable term here, ESRI called it widget.
Sample of experience builder
Sample of web appbuilder