I have an ABolt with a fully rifled barrel, has very good accuracy to 125 yards, haven't really tried beyond that range because don't think it an appropriate shot. Highly recommend it if you can find one--are a bit pricey. Doesn't like 3" shells however, tight head clearance, about welded the first and only I shot into the chamber. Also have a BPS Game Gun (model I have is no longer made, ceased in 2001) with a rifled choke. It is is very close to being as accurate if not as, think you'd need a bench rest to really tell the difference, don't carry one along while hunting so probably doesn't matter.
And a friend has a Mossberg bolt with fully rifled barrel, don't know the model number, but I am impressed with its accuracy as well. Not quite as pretty as the Brownings, but not nearly as expensive either.
Main advice is to get a rifled something, barrel or choke, if accuracy is what you're after I would guess that about any would be better than a smooth barrel. Personally I'm a Browning fan, but alos think my friend's Mossberg bolt is quite ccurate and wouldn't say anything against it.