I'll throw this one out there. There are three types of bunkers - Manicured, Frilly edged, completely "natural".
I class manicured as say Augusta; Natural as like Pine Valley or RCD where the line between maintained turf and completely natural seamlessly blend into each other (and very hard to replicate without it being left to evolve); And lastly Frilly, which is de rigueur right now and is sort of a half way design, with a long fescue edge/faces and the rest is mowed.
I'll say the natural edges are overall more maintenance, which comes from from maintaining courses with both.
The weekly maintenance on the clean designs are more, although newer machinery like the Ventrac has greatly reduced the labor requirements. A quick example was years ago we needed appox 6x12 hours to Flymo and edge bunkers, followed by 2 x12 to clean them out afterwards. That was for one mowing. Now with the Ventrac, its 1x6hrs with the machine, 2x3 for the flymoing and edging and 1x4 to clean them out for the same area. So 16 vs 96 man hours...
Having frilly edges would remove some of the hand work but (and this depends on the design) they would probably still need some weedeating tiding up at least once a month, so there are savings on regular maintenance over the manicured types.
The true natural bunkers may need none of that on a regular basis. However, the issue comes back to letting them evolve. As they mature, the flatter edges grow in, the big face edges collapse and sometimes need shoring up or repair, the plants in the waste areas get bigger etc. All of these things needs cleaning up at least once a year so they don't intrude on play. As PPallotta mentioned there is a fine line between being left alone and left to evolve but left to evolve does need a lot of maintenance to keep the areas playable. Again it depends somewhat on the design and it is offseason work but cleaning up these areas take a considerable amount of manpower so at the end of the year when the amount of hours between both are compared, the natural bunkers will require more hours to be spent on them.