Both design strategies have strengths and weaknesses. AUVs are untethered, and thus have a greater operational radius. Once programmed, they can operate independently, carrying out missions for hours or (for larger vehicles) days. On the other hand, one programming glitch can result in a million-dollar vehicle disappearing into the inky depths, never to be seen again. The ocean is a big place, and if an AUV has a critical failure at any distance from its operational base, then it’s bye-bye AUV. For that reason, many AUV operators in practice keep the AUVs within telemetry range of a crewed vessel or base so that a failed unit can still be recovered by using its last telemetry to locate it.
ROVs by contrast need a guiding hand at all times, which means that every hour of vehicle operation is also an hour of crew time to pay for. On the plus side, ROVs tend to be more maneuverable than AUVs, since human pilots still outperform robots in field conditions.
ROVs and AUVs have a very extensive list of suitable missions. Both have military, commercial, industrial educational, and even recreational uses, and the overlap between the two types of vehicles for specific mission types is very broad. The choice between using an ROV or an AUV for a specific project often comes down to the nitty-gritty details of the mission, or the resources and philosophy of the deploying organization or individual. Both types of vehicles are outstanding at all types of underwater work, and both types of vehicle have areas where they shine a little brighter than the other. ROVs probably have the edge in terms of usability and initial investment; they are simply less expensive, and it is easier to learn how to pilot an ROV than it is to learn how to program an AUV.