For a Ph.d and why?
Thoughts on the original question and also how the DMIN from Liberty or a Ph.d. from the others would look on a college adjunct application? Which would be better?
So long as we keep in mind that academic positions, including adjunct, are becoming rare as hens' teeth, I would always recommend a PhD over a DMin if you're interested in pursuing some kind of an academic position. However, check GT's post. It is full of good recommendations, as usual.
I pastor a church and have a PhD in historical theology from a good school. It hasn't hurt my ability to minister, but enhanced it. However, most guys I sat in seminars with would be unable to make this kind of transition. (Honestly, I didn't either until I had several divine encounters and read a couple influential texts)
My academic goals for teaching would primarily be focused on adjunct work as well. These positions are more available than full time, tenurable positions. Those positions are almost impossible to find and impossible to contend for if you don't have a PhD from Europe or a top-tier school.
As I've encountered these schools and such I think Pretoria or UNISA are good options so long as you understand the issues that go with these kinds of schools. (i.e. they will not be recognized by most university administrations.)
These days if someone wants to go get a DMin I encourage them to either go to Beeson or Gordon-Conwell. Otherwise, their churches and ministries are almost better off by them going and getting a good MBA with an emphasis in leadership or non-profit management.
Of course some folks just want "Dr" in front of their name. Frankly, that's a silly reason to pursue a vapid degree.