What Jack said is true. The AR design is inherently accurate. Typically a $1000-$1500 AR will shoot alongside an extremely worked over (accurized/blueprinted) bolt action gun costing two or three times as much. My Dtech 243WSSM shoots as well at any range as my blueprinted 40X .308 (at considerably less than 1/2 the price). That's pretty normal.
As mentioned, besides the cool factor, follow up shots are easier, maintenance and cleaning are a snap, and almost limitless configurations are easy and relatively cheap (and don't require a gunsmith). You can also change rifles in a matter of a few seconds (literally) by simply changing uppers. A 16" barrel .223 "brush gun" one minute and a full blown long range match rifle (in any number of chamberings) 10 seconds later.
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But their triggers even the after market ones suck compared to a good trigger on a bolt gun. They are heavy. So lots of guys order them with shorter barrels. The result is the bolt gun with the longer barrel is like comparing a regular .223 to a 22-250 you're losing 150 fps plus. I know lots of guys with bolt guns that still get doubles.
The bolt gun is cheaper or you can have one re-barreled and my guess you will have a much higher quality shooting piece of equipment for the same price as a match grade AR.
The aftermarket triggers do NOT suck. I've got Jewell triggers in AR and bolt, and it's as good in the AR as in the bolt, which is to say, they are equally excellent. I can adjust either down to less than 2 oz pull.
A lot of guys do get ARs with short barrels, but it's not usually because of the weight, it's to make it a faster swinging rifle. Remington lists their 700SPS varmint (the equivalent to my WSSM) at 8.5 lbs. My WSSM weighs...8.5 lbs (including sling and slip on butt plate). If I was interested, I could easily drop probably a pound or more by changing the stock, handguard, etc (and still have a bull barreled match grade rifle). The shorty barreled carbine (M4) variant is listed at 5.56 lbs. Weight is not a factor.
By the time you have a bolt gun accurized and re-barreled with a match grade barrel, you will have considerably more money in it than what you will have in a match grade AR, and unless you are talking about a $4000 + benchrest gun, it's very unlikely it will shoot more accurately.
The AR isn't for everybody. They are a little strange ergonomically at first for those of us used to drop comb stocks. Much of that can be "fixed" with stock extensions (or different stocks), high "forward mount" scope rings, etc., but they will still take a little familiarization.