What I mean my push/pull was pulsation.

From driving over 40 or so miles/hr, I would remove my foot from gas pedal and weather I engaged breaks or not, as truck rolled to complete stop it would pulse in a similar pattern as if the rotors were warped. (no matter if I pressed breaks or not)

I can also say that the truck is tighter in the way it moves (quicker and with less lag).

Did I buy the diff used? No, I purchased a brand new unit from BMW. Originally listed for about 2.1k, local dealer advertised it for 1.8k, so my guys got it at lower price.

Diff types. You will have to look by part number. I believe there is a diff on ebay or locally in ATL for a 3.0 car. If that's what you need let me know. I do believe the price was about 1.3k (from what my mechanic told me). At that price I'd rather buy brand new with warranty.

Uhh the warranty: if this part fails again BMW will replace it for free and to include labor.