Both the BG and Shield fill different roles as guns. It's like comparing apples to oranges.
Some people can pull of the Shield with pocket carry, although I could never do it. It's more of a hip gun, whether you choose IWB or OWB.
The BG is more of a deep concealment gun. Pocket carries easily.
To tell you to pick one or the other we would need much more information about what your needs are when carrying, and the expectations that you have when carrying a firearm.
Many shoot the bodyguard pretty good, but the easier gun to shoot of the 2 is going to be the shield. If I personally had to pick one, I'd go with the shield. In fact, I did go back and forth between the BG and Shield for a bit, and I decided that I thought the Shield fit my needs better, and was a better package than the BG for me.