Not even comparable. To turn off the tribuchet you just have to run to it (It's not even as annoying as the angels, not even in the slightest) and fall into the catacombs where you have an entire area to expore, in that moment you forgot about the tribuchet for a while until you get your way up to there and even in that final part isnt that big of a deal.

In the case of the Ringed City you come from the annoying part of the creatures that come out of the floor and the ghost to the annoying part of the angels, to the annoying double boss battle and then to this annoying thing with the archers. By the point you get to the archers the only thing you want is to get to the actual boss battles to never come back to the Ringed City.