The LM2596 based modules will handle far more current than the LM317 based modules. They are two totally different types of power conversion. The efficiency of the LM2596 based modules will be in the 85-90% range. The efficiency of the LM317 based module varies based on the input voltage, but it'll be MUCH lower, sometimes down in the 20% range.
All the input power that isn't delivered to the load is dissipated as heat, which is sometimes a major issue.
I have some LM317 based modules, with any significant current draw through them, the heatsink gets pistol hot! I've used the small LM2596 modules to supply 1/2A to a smoke unit, it's still barely above room temperature.
Take the ratings that you see in the eBay ads with a grain of salt, they are stated under ideal conditions. The 1A for the LM317 modules is with a minimal input/output voltage differential to minimize the power dissipation, in the real world, that rarely happens.