According to Phone Arena ( LG Optimus 2X vs Motorola DROID BIONIC vs Atrix 4G: specs comparison - Phone Arena ) The difference between the DROID BIONIC and the AT&T Counterpart is:
Bionic will have 4.3 inch screen, Atrix will have 4.0.
Atrix has 1Ghz RAM (needed for the laptop dock, and from what I've heard the extra 512MB's of RAM can't be used except with the dock), Bionic has 512 MB's.
Both have nVdia Dual Core Tegra 2 processors.
Atrix has a finger print scanner, Bionic doesn't.
Bionic will have an 8MP camera, Atrix will have 5MP.
Both are made by Motorola.
Post more differences and I'll add them.