Both offer the same functionality, but setting up a dropin is easier (there is a user interface for it). Beware that at this time, Sysv init script (Unix System V style) shipped by all distributions are very limited in functionality. The following document shows how you can enhance the current script you have:
http://www.solucorp.qc.ca/linuxconf/tech/enhsysv
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 yet keeping it compatible in case of an upgrade.