I just use a 30cal brush and scrub around in circles. Then, to get the neck area, I twist the brush in and it gets that part.
To mop it out, I use a .45cal mop. Tight fit, but works fine. For the lugs, I just use a nylon brush / toothbrush. This is when I do minor cleaning after short-sessions. I use brake cleaner for serious cleaning after longer sessions.
The key is to get the crud out before having to brush. Invest in BRAKE CLEANER. If you have optics, you might want to protect them or buy a synthetic-safe cleaner. My optics are on quick-detach, so I take them off. Wal-Mart sells brake cleaner for $3 a can. Well worth it. Just blast away with full-power. Wear EYE protection or it will fly back at you, especially when getting the lug area.
I also blast the bolt and carrier with brake cleaner. After I am done, I check for any hardened crud, and that's when I go to the brush - if needed. Then I spray CLP all over it and over any dry areas that should be lubed. There's almost always an excess of oil because my aerosol can of CLP dispenses way too much. I take my aircompressor and blast off any excess. This is good, because it spreads the oil thinly and evenly over the entire surface of that which I am trying to lube. It also forces the oil into every little space. My entire bolt, carrier and interior of upper is lightly coated by CLP. No drips, no dry areas. Just right. It has the perfect film of lube and the "wet" look.
Whole process takes 15 minutes tops. I'd say, the brake cleaner cleaning takes 2 minutes. Any brushing/mopping of tough crud, probably 5-7 minutes. Rest of time is spent on oiling and compressed air.
Cleaning the bore is seperate. I usually use a copper cutter with a rod/brush and scrub away. I have a patch-worm and I pull patches out till clean. This takes about 10-15 minutes.
Beyond that, the AR is clean. Nothing else really.