Schottky diodes are pretty much fleshed out, there isn't much give-or-take in characteristics. 1N5819, MBR340 and so on are still pretty much current technology, even since they were introduced however many decades ago.
The difference between types pretty much comes down to a single parameter: a lower barrier has less forward voltage drop, but leaks more and breaks down at a lower voltage. A higher barrier has higher breakdown and less leakage, but more forward drop.
The only relatively new things are superbarrier and TrenchMOS type schottky, which extend the reverse voltage and improve leakage current, at some expense to the forward voltage drop.
What are you trying to do? If it's power rectification, use a synchronous rectifier (or just deal with it, 0.4V out of 5V isn't terrifically bad, even for battery operated equipment). If it's for signals, use junction diodes and a precision rectifier circuit; if the additional forward drop is a problem (for instance, it won't go within Vf of the supply rails), choose a lower amplitude for the signal path so it's not clipping.
Tim