Interior drain tile with a sump manages water that has already reached the wall and is the common solution here. Exterior excavation stops it before it arrives and costs several times more. Most homes are served correctly by interior work.
More detail
These are genuinely different approaches to the same problem and contractors specializing in each will tell you theirs is the right one, so it is worth understanding what each does. Interior drain tile is installed by breaking out a strip of the basement slab around the perimeter, laying perforated pipe in gravel below the slab level, connecting it to a sump basin, and re-pouring the concrete. Water that reaches the footing is intercepted and routed to the sump rather than rising through the cove joint. It usually includes a wall vapor barrier that directs wall seepage down into the system. It manages water rather than excluding it, and it is done from inside so landscaping, drives, and decks stay intact. Exterior waterproofing means excavating down to the footing around the outside, cleaning the wall, applying a membrane or coating, installing footing drains in gravel, and backfilling. It stops water before it reaches the wall, which is the ideal in principle. In practice it costs several times more, it requires access all the way around, and anything in the way (a driveway, a deck, mature plantings, a neighbor's property line) either gets removed or blocks the job. When exterior is genuinely the right call: a structural wall repair that requires excavation anyway, a foundation with no footing drains that is being fully rebuilt, or a situation where interior work has been done correctly and failed. For the great majority of homes with cove-joint seepage or wall weeping, interior drain tile with a properly sized sump and a battery backup is the correct and proportionate answer. A contractor recommending full exterior excavation for a straightforward seepage problem should be able to say specifically why interior work would not serve.