Welcome to TFL, rmatney!
As much as I love my Glock, and I do, I'd go with the Shield, all other things being equal. You want it for a CC gun. To my mind, that means that you need a pistol that's had all of the kinks worked out. I'm not convinced that the G43 fits that description. The Shield, on the other hand, has been around for a few years, so I'd be more likely to think that it has.
Also, there are pistols with manual safeties, pistols without manual safeties, and pistols that can be had either way. If you're more comfortable with a manual safety, get a pistol that has one.
Finally, go try to find a shop that has both. Hold them & see how they feel in the hand. Better yet, if you can rent them and shoot 'em side by side, do so. Only you can decide how a gun feels in your hand, how well you shoot them, how much you like shooting them, etc.
ETA: My advice is worth exactly what you've paid for it. I haven't shot either one of those pistols. I've held a Shield, but not a G43, for whatever that's worth.