An internal drive is faster than an external one. The internal drive can use DMA transfers to move data from your hard drive to your burner. The external drive has to use a PIO-type transfer, which has more communication overhead than DMA. The difference shouldn't be very large, though.
An external drive is more convenient, as it can easily be moved from one computer to another. If you have an older notebook, this may be the only way to add a DVD burner to it.