The Shield is a subcompact 9mm with the ability to mount an optic. The Bodyguard 2.0 is a .380 pocket pistol. Either one can stop a fight just fine and while some folks do carry their Bodyguards in belt holsters, I think it does its best work as a pocket pistol, to be carried in a pocket when you're "not carrying a gun" for whatever reason.
I did not like the factory sights that came on the Bodyguard. Mine came mounted off-center but even if they weren't, I'm not a fan of their design. My Bodyguard is also picky as fuck about what it feeds. I've only gotten 2 of the 7 types of HPs I've tried to reliably feed in it. I'll probably just run ball ammo in it. The Shield eats whatever.