Size wise, the P938 is significantly smaller. To some, that will make the decision right there. I have one and I love it. Runs like a hose. I drop it in my back jeans pocket for very light duty when I just don't want to holster a gun for whatever reason. (Rare, as the pocket size guns are back-up guns in my view, not up to snuff as a primary.)
BUT, I would not recommend either of the P938 nor the Shield as a primary carry gun, as the G26 and M&P 9C offer much more for not much of a bump in size.
You carry a gun so that if your worst nightmare comes true and you find yourself facing evil up close and personal, you will have the best chance of prevailing against 1, perhaps 2 or more threats. In such a case, you would pray to have at LEAST 10+1, 12+1, or much better 15+1 or 17+1 rounds on tap. Last thing you want is to be at slide lock when adversaries have more rounds on tap heading your way.
Carry the most gun you can, not the smallest, lightest gun you can.
The Shield is a fine pistol, but for me, it's not small enough to drop into my back pocket like the P938 is, nor is it as capable as the G26 or 9C is. The Shield is a 'tweener' gun in my view and is a lesser choice than either... In my view.
My recommendation would be to carry a G19 because it carries like its not even there, is stone reliable, accurate, and has 15+1 rounds on tap. This is why the G19 is so overwhelmingly popular as a carry gun. It's barely bigger than a 9C, yet has a significant capacity advantage. Sweet deal.
I usually carry a G17 or a G19, rarely... a G26 if I want smaller and lighter, but the size difference is so minimal that the G19 still makes more sense.
Ask yourself why a Shield vs. a 9C? Are you simply unable to carry a 9C or a G26 for some reason?
If you're going with holster carry, why not gain the potentially very significant benefit of greater capacity? The difference in ability to carry is insignificant.