Differential or Power Transfer Unit
 

About 3 weeks ago, as I was driving, my car started to violently shake, it seized up and stalled. I checked the oil (I knew I had a slow leak) and it was completely empty. I added a few quarts, restarted, let it run, and attempted to drive. It again shuttered, seized and stalled.
The mechanic I took it to, checked it all over, replaced the rotor clips and brake pads and said it ran fine. He drove it around for 2 days and it never stalled for him.
It had a slight humming noise from the time I picked it up.
2 days later as I was driving, the humming noise got louder, the car shuttered and stalled.
I took it to a 2nd mechanic (he too said it was running fine). He drove it around for a day and said it never stalled for him. I explained all the symptoms and he did some research and said it was the Power Transfer Unit. He added gear fluid but said it did not help the humming.
I had also done some research, but found more matching symptoms for the differential.
How would I know which it is?