Both offer the same functionality, but setting up a dropin is easier (somce there is a user interface for it). Be aware that at this time, the SysV init script (UNIX System V style) shipped by all distributions is very limited in functionality. The following document shows how you can enhance the current script you have:
If you give an add-on the same name as a SysV init script, the add-on will have precedence. The script won't be called anymore. Quite often, one will create a dropin and will simply define the start, stop and reload commands by calling the SysV script. This is an easy way to enhance a SysV script without touching it, and also keeping it compatible in case of an upgrade.