The largest (and in my oppinion only) disadvantage of an external drive for backups is speed. Particularly USB externals take forever to backup a large amount of data. Internal drives, or external drives that have an ESATA port (if your computers support it) are the best performers.
My preference is to go with external drives for security. Typically, when your done backing up you unplug the drive and store it somewhere. That keeps your data save in the event of a power surge or a very serious virus attack which is something internal drives are not protected against.