Well, most weapons are better than the bowgun, but remember that Claire also has early access to the grenade launcher, which comes with three different ammo types and is much more reliable for killing stronger enemies than the shotgun (unless it's filled with explosive rounds, which have such a ridiculously short range that they could almost pass as a melee weapon). Leon has to rely on the shotgun, his only (moderately) strong weapon until he finds the magnum much later, so I'd say his scenario is actually the harder one.
But you're right, if I had to choose between bowgun and shotgun, I would definitely go for the latter, especially in the newer games. Ada's RE6 campaign was a pain in the ass for me at first thanks to her terrible weapons, a pea shooter that barely damages anything bigger than a rat and a powerful, but extremely slow bowgun - I was so happy when I found the shotgun later in her first chapter!
