Bryan,
We can't tell you which one to buy. What I like, you may hate. You really need to shoot both of them. Look at availability of accessories (holsters, extra mags. etc). I would also look at the weight of each gun and the capacity. If you have a bad back or wear lighter weight clothes, a lighter weight gun might work better for you. Lots of people have no problems carrying full sized 1911's. Others prefer a single stack light weight gun. I have and carry both a double stack gun (M&P 9c) and a single stack Sig. p938.
People love both of the guns you listed. My daughter's boyfriend just bought a XDS in 9mm for his CC gun and loves it. He had my daughter shoot it and she really liked it and did well with it. I was going to get a XDS because I really liked how the trigger felt, this was pre recall. After the recall, I hated how the trigger felt. But that is just me.
When I was looking at a lighter weight option the Shield was recommended to me, I just can't get into the Shield, it does nothing for me. That is why I got the Sig. Lots of Shield lovers here though.
Again, you have to shoot both. Look at concealability of both. Look at reviews, I like to watch youtube videos and read the comments below. Google, gun X and problems. See which gun feels better in your hand. We can only offer you our opinions as to what works best for us, but each person is different. For every 5 people who say get the Shield on the M&P forum, there will be 5 (on the Springfield forum) who will say get the XDS.