I use both sorta kinda. I tend to lean towards the Bore Snake. I have a one piece stainless steel cleaning rod. I'd suggest the single piece as opposed to a 3 piece rod that I have previously used for years. The 3 piece ones do tend to misalign and the you wouldn't want that edge to dig into the bore or the edge of one flare out and get that to gauge into your barrel. My one piece rod has had spiral scratches gauged into it so I believe it is possible. Get a polymer coated one and only use brass rod ends. Plastic do wear out and would bend if you push a patch through sometimes getting binded. If you try to pull out a plastic eye end the threads may strip and you'll haave to push is out one way or another. Don't use the patch push ends in rifles!!!! The are pretty much for pistols or larger bore rifles or muzzle loader types.
With chorme lined bores it is not necessary to do the complete cleaning ritual of solvent, bore brush, patches until they come out clean. In the Army it used to be (maybe still now) a soldier had to clean that weapon until it can nearly pass white glove inspection. That type of cleaning was instilled in me and to some extent I still follow that doctrine but I adapted it to a better result. It's called gun cleaning OCD. Trying to clean weapons to that degree will only accelerate wear specially when it comes to the M16 DI systems-specifically where the carbon ends inside of the bolt carrier and the methods we used to use to remove it. I no longer do that type of standard. I would let the bolt carrier soak in CLP (still the best for this) over night or something like Sweet's for a few hours. But that was the M16/AR.
As far as I would clean my XCR barrel I run a few patches soaked in Sweet's bore cleaner or Hoppe's from chamber to muzzle and just use a bore snake 5 to 10 times chamber to muzzle. If I use Sweet's I still run a patch with Hoppe's or CLP and then a couple of times with the bore snake dry. On a chrome lined barrel a bore brush is not necessary. The Bore Snake has some bore brissles and that is enough to get into the rifle grooves. I don't like to leave any traces of Sweet's without using Hoppe's or CLP afterwards b/c Sweet's is corrosive to copper and it is nearly impossible to remove all copper left in the rifling grooves, so the Hoppe's or CLP acts as a neutralizer. If you use Sweet's (or other ammonia based solvents-you'll be able to tell by the cat piss smell) you will notice patches that you pass through come out turquoise colored. This is the solvent dissolving the copper and it is the first stage of copper corrossion. If it is not completely removed the remaining copper will continue the corrosion process and it will etch into the barrel metal or chrome lining. That will also lead into bi-metal corrosion process (takes a while). Hoppe's solvent can be left in the barrel because it had lubricating properties in the solvent.
The XCR is a combat rifle, but it is a dream to clean compared to the AR. The only carbon retentive parts is the gas block and gas plug assembly and the gas piston specially the inside. What is cool about the XCR specifically is you don't have to return that gas piston to complete shiny like-new condition. Soak those parts in solvent or CLP and remove as much as you can. Then wipe dry and put together dry. I usually just drop the smaller gas pieces in to an extra Hoppe's or Sweet's jar, or use a small container full of CLP. I then use needle nose plier or my dental tool pick (only needed to clean my AR) to retrieve them after it has soaked for a while. Try to get an extra bottle of solvent to use it specifically for that.
A 3 piece rod was handy for field cleaning purpose but now Bore Snake does 2 jobs in one for field purposes. A cleaning rod would still be needed to pop out anything stuck in the chamber or barrel that can't be dealt with a snake, so don't throw them away! Otis makes the coolest compact cleaning kit. I had one but it got lost in the field. The pull though cable would handle anything and almost made the rod obsolete, but as I mentioned above not quite yet. The Bore Snake would make cleaning patches obsolete and the Bore Snake can be cleaned by simply soaking it in hot water and detergent and hand washing it (don't put it in a washer unless you want to spend an hour unwrapping it from the base of the agitator!) then put it out to dry in the sun. In an infantry squad an Otis kit and Bore Snake per soldier and 1 cleaning rod per squad is all what would be needed.