I own a Savage 99 in .308, a Winchester (Browning) 1895 in 30-06 and am eyeing the Henry box mag .308. Any of them could be "accurized" to near bolt gun standards, but that is not what they are for. They provide excellent hunting weapons.
The only lever gun contests I know of is cowboy action shooting which is a test of more than weapon accuracy, they even get points for style!