No truism is nearly so elegant as, or responsible for more deep insights than, Bayes's Theorem.
The second is a graphic rendering of a particular Bayesian problem. I adapted it from an article by Spiegelhalter et al. in Science.
In my view, the "prior odds x likelihood ratio = posterior odds" rendering of Bayes is definitely the most intuitive and tractable. It's really hard to figure out what people who use other renderings are trying to do besides frustrate their audience or make them feel dumb, at least if they are communicating with those who aren't used to manipulating abstract mathematical formuale. As the graphic illustrates, the "odds" or "likelihood ratio" formalization, in addition to being simple, is the one that best fits with the heuristic of converting the elements of Bayes into natural frequencies, which is an empirically proven method for teaching anyone -- from elementary school children (or at least law students!) to national security intelligence analysts-- how to handle conditional probability.
If you don't get Bayes, it's not your fault. It's the fault of whoever was using it to communicate an idea to you.
Spiegelhalter, D., Pearson, M. & Short, I. Visualizing Uncertainty About the Future. Science 333, 1393-1400 (2011).