While it has many uses, a carriage stop is typically used to turn or bore to a precise depth. Most commonly, you would set the stop in the desired position and power feed almost up to the stop and disengage the power feed, then manually feed up to the stop. This has several benefits: one, you don't knock the stop out of position, two, you don't stress your feed gears, three, you don't wear the feed clutch prematurely so that it eventually slips on standard cuts. You can use a stop in combination with the feed clutch; that's up to you but most of us don't do that.
Most of the time, you will use your saddle handwheel or a DRO to move the saddle to the desired location and then move the carriage stop into position and lock it down. If I need great precision, as in a precision bore, then I trust an indicator before I would trust a micrometer carriage stop. Anyway, then you move the saddle back, engage your cutting tool and cut up to the stop.
My Emco 11" lathe has a feed clutch at the end of the drive rod. I think its a useful thing to have to save my gear train in case of an accident but I don't abuse it. My manual states it can be used with the stop for precision boring but doesn't mean I'd do it that way. The manual also says the stop can be used to prevent a crash when the lathe is used by an apprentice. Interestingly, I do use it that way when I'm machining up close to the chuck (feeding manually). Here, I mean when the cutter is inside of 0.005" of the chuck jaws and a crash would be catastrophic.
I guess my point is that the feed clutch is useful in a crash or if taking too ambitious of a cut; it will slip before excessive damage is done to the gear train. A carriage stop is a must have for precision turning and boring. Using them together can be done but it can also be done manually, with less wear and tear to your lathe.