Here's my long winded opinion of Minnemann vs Mangini.
I find Mangini to be boring. He's definitely a very good drummer, and I'm sure other people really love him, as evidenced by the fact that he's a drum teacher, and he played with Steve Vai and other big projects. He's also programmed frickin' missles, and it would be interesting to have a computer science graduate in DT. But I think DT needs something extra, something spontaneous and creative and humorous. Mangini just feels like a session drummer in any video I see him. I've never seen him to do an interesting and original roll or beat, and his showoff bits are often based around playing fast. And honestly, in that regard it's hard to beat a lot of little known death/black metal drummers, who probably didn't go against Mangini in a formal speed test, but there are lots examples of drummers playing way faster.
Minnemann is nuts. He experiments with his kit, he plays around with samples (he frickin' drums to VOICES). He seems like a fun guy to hang around, and he's got a cool accent. Every single time I've seen him play, he did something original, and didn't stop at just playing a beat, he added something to it. I also really like his drum sound, compared to Mangini, especially his bass drum. To me, Minnemann is a cross between Gavin Harrison (imo the best drummer around right now in the prog world), who probably wouldn't play in DT because he's too jazz oriented, and Mike Portnoy who is often times "to the point", and likes his metul. So, Minnemann falls somewhere more towards proggy drumming than Mangini, and somewhere between MP and Gavin Harrison in terms of technique. I really hope he's the new drummer, but it seems at this point that Mike Mangini may have gotten it, in which case, I'm still going to be excited, but if Minnemann is the choice, I will rejoice.