Both will import just fine. It’s really a matter of what works best in the given situation. For instance, in your example the connected branch will be easier to texture without creating a visible seam where the branch intersects the trunk.
There are a lot of cases where unconnected vertices are useful as well though (foliage billboards, for instance) It really just depends on your specific use cases. Hope that helps!
I personally tend to model my branches unconnected so that I can duplicate and move them around in blender to create the whole tree.