Two main differences come to mind. The Marine Corps version usually had a high air intake which was for the purpose of fording streams which is pretty comical for an up-armored vehicle. Also, the Marine Corp M1151 was usually equipped with the Marine Corps' MCTAGS (Marine Corps Transparent Armored Gun Shield) turret while the Army used the OGPK (Objective Gunner Protection Kit).
The easiest way I know to tell the difference between a MCTAGS (made by BAE) and an OGPK is that the panes of ballistic glass in the front are high on a MCTAGS and low on an OGPK.
The picture below is of a Marine Corps M1151 that is equipped with a Chameleon jammer and the high air intake fording kit (which I don't believe the Army variants had).
This is an OGPK
There were also a variety of door and window configurations used on the M1151. I am not sure which ones were specific to the Marine Corps versus the Army.
This is a Marine Corps variant with two pane side windows followed by a picture of an Army variant with single pane side windows. Note the different in the air intakes. Note also that the OGPK in this photo of the Army M1151 has overhead protection for the gunner as well.
By 2009 the Marine Corps and Army were trading rebuilt HMMWVs that were rebuilt by the Army at Taji and we had a mixture of MCTAGS and OGPK turrets in II MEF (Fwd). Maintaining configuration control was really difficult because there were not enough spare parts to repair either the MCTAGS or the OGPKs at the time.
The armor added to these vehicles above the normal un-armored HMMWV had really serious adverse impact on performance and safety. Rollovers are common because of the body roll and center of gravity. Braking and acceleration is horrible. The wear on the brake pads resulting from the excess weight resulted in a thumb rule that you had to replace the brake pads as often as you had to change the oil. They also needed huge coolers for the transmission as well as the engine coolant.
Despite all the protection offered from side impact blast and projectiles these vehicles were barely more survivable that an unarmored HMMWV for an underbelly blast. They are sub-optimal in almost every respect.