The comparison is not exactly apples to apples but......

The Lincoln 350MP is a multi-process CC/CV power supply that can run SMAW and GTAW as well as GMAW/FCAW. This is reflected in the rather significant price difference between the two.

350P is strictly GMAW/FCAW

I have run 350P and Lincoln Powerwave 355 head to head and find them both top shelf....

Lincoln 350MP has Pulse on Pulse... Which may or may not be valuable to your alum operatons.

Miller 350P has a four drive roll setup and the 350MP only has two... This is significant to me. With a push pull gun it's not such a big issue but for steels and FCAW it is.

They both have different pulse programming operator interface styles... Both are fairly easy but some operators favor one over the other. (I'm ambivilant)

I don't think you would be disappoianted by either... Semi Auto Synergic GMAWP technology has made it's biggest strides in the last 3 years and both of the power supplies you mention are great examples of the excellence now attainable at at about 1/3 to 1/2 the price of what inferior machines were producing not that long ago.

Why not have your reps demo each for you before you buy....  ?