Cave Story ~ Convenient Edition is a mod of the 2004 freeware version of Cave Story made with the intent to provide a convenient and easy way to play the game in modern times. The mod consists of selected parts of Clownacy's DLL Mod Loader and some very small fixes that have been applied to the graphics and translation.
Fullscreen, frame rate, and controller support have been improved. Outside of these things, there are no major changes or additions to the game. If you are interested in just playing the original Cave Story without any of the hassle that stems from its age, I would personally recommend this mod.