If two theories could not, for practical reasons, be tested one should prefer the one with the highest degree of empirical content, said Popper in The Logic of Scientific Discovery.
Many have sympathized with this view, but the problem is that the idea of simplicity is highly intuitive and even personal, and that no one has managed to formulate it in precise and acceptable terms.
Popper's solution was subsequently criticized by Thomas S. Kuhn in The Structure of Scientific Revolutions.
He denied that competing theories (or paradigms) could be compared in the way that Popper had claimed, and substituted instead what can be briefly described as pragmatic success.
The main criteria usually proposed are to choose the theory which provides the best (and novel) predictions, the one with the highest explanatory potential, the one which offers better problems or the most elegant and simple one.