Is the slide/ barrel on the shield the same as the one on the M&P compact model? I'm thinking yes simply because of the manufacturing economies but this is a WAG.

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No.

I own all 3 (full size, compact, and shield) and the compact slide has the same dimensions as the full size except for length.

S&W's website should have all dimensions of all guns on it.

No. The slide and barrel on the Shield are smaller than the compact model. The width is the biggest difference between the two.