They can be about as accurate as jacketed, if the proper hardness of alloy is used, and velocity stays sane. They can certainly be alot more accurate than anyone I know can hold, unless using a bench rest.
I use a 185 grain gas checked round nose for reaching out to the 200 yard line, and a 93 grain .32 caliber round nose pistol bullet over bullseye for short range plinking loads (25-75 yards). I'm not getting world class accuracy, but I hit what I shoot at (clays and whatnot), and it's fun to shoot without Stre$$ing out about my university students budget, and after all, I'm shooting a 100 dollar sporter, not an anshutz.
I also don't use a scope much, so I don't try to hit dimes at 100 yards. I hit a can of sodapop spray-painted blaze orange at the 125 yard line on the first try, offhand; when I was out with my buddies once. (offhand from the seated position, I'm in a wheelchair)