My suggestion is to change the behavior so that the text of the link is selected by default instead of dragging the whole link. Then the whole links could be dragged the same way as with dragging normal text: select the text of the link and then drag it. Or by using a modifier key (like the ALT-key now for text selection) to toggle the drag behavior.
But I think I'm missing something important why the default behavior is what it is? Maybe a preference could be added to control the behavior.
On bugzilla I found this related bug: bug #378775
It is about implementing the same behavior that was in the old Opera which was a compromise between the two operations:
vertical drag = drag whole link
horizontal drag = select text of the link
I think this is too complicated and causes confusion.
Safaris text selection was also described in this comment (it is not used for links):
https://bugzilla.mozilla.org/show_bug.cgi?id=378775#c10
if you hold down the mouse button over a text selection and drag right away, it will start a new text selection; if you hold down the button and wait a bit, it will drag the selection.