Major advantage of the drops is, as WDT notes, bottling just a few before sending the rest into the keg, because you toss one in a bottle and fill. However, the drops vary by manufacturer for intended size of bottle, certain styles of beer have certain amounts of carbonation with them, and people like certain amounts of carbonation, which is the big problem of drops of less control (a drop may be enough for a 12oz but a little much for 22oz and not enough for 750ml, for instance). Also, when bottling batches, the drops require more active time but less passive time (sugars require a little bit of time to boil and then transferring into a bottling bucket, but you simply set and forget those).
Nothing stops you from using either as the situation calls, but I would recommend getting accustom to using sugars because you can do things such as candied sugars and honey to add additional flavors, and the process becomes familiar.
