Suppose we have two scientific theories A and B. They have different postulates but both make the same predictions. If the selection can not be taken out by Ochkam razor then how we select what theory we should dismiss ?
If there are two distinct theories that are functionally equivalent — i.e. that make the same predictions, produce the same results, can be verified by the same empirical observations, etc — then why does it matter which we choose? The choice is aesthetic, not analytical. We might choose to use one theory in one case and the other theory in a different case, because one or the other is easier to use, more compact, more pragmatic, more 'elegant,' or has some other pleasing quality within a particular context. Granted, in most cases the decision would be made for us by convention: previous researchers would have decided to use this theory or that one for reasons of their own, and we follow suit out of habit and training. But that is merely a historical artifact, not an analytical decision.
Please note that Occam's Razor is itself an entirely aesthetic choice, not an analytical one. There's no logical reason why the theory with the least number of premises must be the better one, but in the absence of other distinguishing features the more compact theory is more pleasing to the eye.
The only analytical way to distinguish between two theories is to find a real-world condition in which — theoretically speaking — the theories ought to produce different measurable outcomes, and then instantiate that condition to see which measurement holds. That is not always possible (at least within a given technological framework), and when it's not possible we make non-analytical choices as we see fit. A theory is merely a model, and we can have as many different models of a thing as we like so long as they don't contradict each other.
Taking your example of the two "equivalent" theories (which we will assume are both mathematical models), one will be favored over the other for the following reasons:
1) One model makes testable predictions that the other one does not,
2) One model successfully accounts for observations and data collected in the past, which the other one does not, and/or
3) One model is computationally easier to work with than the other one.
If the question at hand is one of modeling, you will likely keep them all as a "toolbox" and use whichever one lends itself best to solving a particular problem. A good example is Newtonian, Lagrangian, and Hamiltonian mechanics. They are all "correct" but they are all also only models of what is "actually happening." They all give the same answers and are mathematically equivalent. However, they sound very different and represent different ways of thinking about the same thing---you just use whatever works best, case-by-case.
Obviously there are many other kinds of theories. But I'd say that generally if you have no way to decide, "keep 'em both" is a good option until you get more information.