A car service or taxi from MCO to BWV will cost around $60 to $70 (plus a customary 15-20% tip) one-way. DME is free, except that it's appropriate to tip if the driver handles your bags.
DME will almost certainly take more time. During normal hours, each DME coach will go to several Disney resorts in the same part of the WDW property. Late at night, the stops can be all over the property. And, as maxiesmom noted, a taxi will leave right away, but DME usually involves waiting before the coach is dispatched.
My choice would be to take the DME coach and read a book or listen to a podcast -- even if it means possibly getting to BWV an hour later than if I had taken a taxi. I'd rather spend my money on something else.
However, I can also understand why someone would opt to pay for direct car or taxi transportation instead of using DME for free, especially late at night.