1. Are Part-Time programs really that much easier to get into, or are Acceptance Rates higher for Part-Time Applicants largely due to the average applicant being more qualified?
I think it largely depends on the applicant pool. A full time program will attract many people from around the country (or even the world) whereas a part-time program will attract applications from the area/region (since they will most likely live within a few hours drive). Because of that difference, the full-time program will have higher average GMAT and GPA because the adcoms can be more selective. But with the part-time program you'll have a smaller pool and probably lower average GMAT/GPA.
2. If Part-Time programs really are vastly easier to get into, why don't more applicants go the Part-Time route?
What to do you want to do with your MBA? Are you a career changer (i.e. engineer to private equity)? If so, you want to go full time so you can get the all-important internship. Without it, such transitions are near impossible.
Or perhaps you would just like to make that leap into the management ranks, but stay within your industry and function? Then a PT program would work since you can get more experience from still working, and learn all of what the MBA offers.
Also, depending on the school, they may not let PT students participate in recruiting events for full time positions. So if you do want to find a new job post-MBA, it's in your interests to go full time. Your target schools should have this sort of information made available online or would be happy to answer any questions via email or information session.
Hope this helps. I look forward to others' input as well.