The Body Guard has a more room in the trigger guard which is good for people with large hands. I've seen people who go with the Taurus TCP over the LCP for this reason (trigger on the LCP "pinches" them). The Body Guard does feel well and fills out more in the person's hand but the LCP is a tad more stream line so it works extra well as a pocket carry piece.
And I've heard the Body Guard groups extremely well.
However, I've shot the BG and I had a problem with my wrist snapping when the trigger breaks (damn double action triggers) and my shots were low. This made me focus on not hitting the target instead of my grouping, but if I remember right the group wasn't bad for a pocket pistol.
The BG has a slide lock safety though while the LCP has no safety (which freaks some people out).
One factor you need to think about is "what are these pistols intended for?". Both are extremely close range pistols, light weight, quick draw, and meant to be a personal protection piece, not a practice gun. Both will work fine, and both come from companies with great warranties and a great reputation.
Just go with the one that fits you better, and that you feel most comfortable with.