I'm not 100% sure of the terminology you are using, so I'll use slightly different terms in my reply.
You can use "very stiff elements" to make the displacements of some nodes geometrically dependent upon the displacements of other nodes. A certain amount of care is required in deciding how stiff is "very stiff". Get it too small and the answer will not be exactly correct. Get it too big and you might introduce ill-conditioning into your resulting global-stiffness-matrix equation system. (This latter problem is less likely these days because most software uses double-precision arithmetic, but the risk still exists.)
"Constraint equations" are a different approach to achieving the same end effect. The required relationship(s) between the nodal displacements are expressed as simple equations, and these equations are used to reduce the size of the global-stiffness-matrix equation system before the solution begins. Thus the possibility of ill-conditioning is completely bypassed. As a side benefit you are solving a smaller stiffness matrix, but in most cases the time savings is too small to measure.
Sometimes the required geometric dependency can only be modelled with very stiff elements, sometimes only with constraint equations. This depends on the type of dependency and on the software you are using. If your dependency can be modelled either way, as a general rule you should use constraint equations. However be aware that with some software the constraint equation approach will not give you the internal forces required to enforce the constraint.