Well, I think crossbows should be stronger if your Archery skill is low.
The thing is, crossbow doesn't require any training to use it properly. You just need the strength to reload the bolt, aim and shoot. Pretty much a gun without gunpowder. So Archery skill shouldn't affect your effectiveness with crossbow at all.
In terms of balance, crossbow is pretty strong and fairly accurate but not as accurate as bows since arrows actually 'swim' through the air. Crossbow is usually pre-loaded so you could shoot it as soon as you take it out although that would make it less accurate. When it comes to reloading crossbow, it should take longer than a bow. Reloading it should be even longer if you are running or moving in general. Crossbow is also much heavier than bow. The damage should be a set number. Since it has no skill to make it more efficient, it should be for people who prefers melee and only takes it out just to shoot out a dragon off the sky.
As for bow, it should be able to shoot faster but you need to pull the arrow back longer to make it stronger than the crossbow. It should be more accurate and you can whack your opponent with your bow if he comes too close. (This has been confirmed!) Crossbow is too heavy for melee attack. As your archery skill grows, your bow should be even more efficient than crossbow, eventually. It's been confirmed that there's two types of bow: longbow and shortbow. I think their difference are fairly obvious.
I think this way, crossbow would find its place in the game WITHOUT completely replacing bow and arrow.