Most oral joint supplements actually have no independent clinical research behind them and some don't even have the same concentrations of supplements that they claim to. Basically when feeding this stuff you might as well be feeding your horse table salt. Corta-FLX and Corta-RX actually have some studies done with them and they showed that the results from these products are there, but they are not huge. In general, with all of these products any results you are going to see are going to be the result of a placebo in you and possibly minor improvements in the horse. Every product is going to work differently with every horse, so what may seem to work for your horse might do nothing for another.
The best and most highly recommended course of treatment (and even prevention) for arthritis or other joint diseases is IV injections of Legend which can be combined with IM Adequan. In very progressed cases of arthritis, daily NSAIDs can also be recommended.