Intersecting surfaces over the curve intersection

Just to clarify, I think you are asking for a comparison between "curve-curve" intersection and a "surf-surf" intersection?

Those aren't official names- that's just the way I think of the two methods.
I've done quite a few of both and don't have a strong preference with either method.  The curve-curve intersection has fewer features in the model tree and the two curves are automatically hidden. (good or bad).

In some ways I like using the surface-surface intersection because of the visibility it provides as to what is happening especially when learning.  That visibility might be useful when someone else works on your part so they can understand what is going on.  It does however create some surfaces that you need to hide or put on a layer - not a big deal.

The surface-surface intersect is also useful if the surfaces intersect more than once because one of the surfaces "loops back" and touches the other surface again.  Good visibility- you can see what's happening.  You can also trim the surfaces ahead of the surface-surface intersection feature to prevent that from happening if needed.