The barrel is slightly tapered because silhouette rules specify that hunter class rifles have to have a tapered barrel. Not how much, but that it is.
I don't know if you plan to use the rifle for silhouette competition, if so, be aware of a few things. If the stock doesn't fit you, you are stuck with it unless you are OK with modifying/hacking on it. This isn't a big deal but a better way to go is to buy a barreled action for a grand and then get a Treebone stock in the Mark Farr design or find an old actual Farr stock. They aren't made anymore.
I don't know what kind of trigger is in the Cooper but Anschutz two stage triggers are simply the best.
Personally, I would get the Anschutz. There are very few Coopers on the line at silhouette and smallbore matches. I suspect that this is due to the superior two stage triggers and the perinial award winning 54 action and high quality barrels.