A common mis-conception I've read around various music forums about this gig is most people are just focused on who has the most technical ability.
To the point John Petrucci posted on his forum that they are looking for three things:
1) Technical ability
2) Someone who can bring a metal attitude to the songs
3) Some who can groove.
Another mis-conception is that Mike was the metal fan, and the new guy doesn't have to be into metal, but that ignores a lot of evidence like:
1) Petrucci, Myung and Portnoy formed the nucleus of what would later become Dream Theater playing Iron Maiden covers .
2) Petricci once said his dream gig would be to replace Kirk Hammet in Metallica
3) James Labrie's lastest solo album incorporates melodic death metal elements
4) James Labrie was wearing a Napalm Death t-shirt in the very 1st Dream Theater video.
Not to mention the rest of band writing the heavy songs over DT's career.
Another thing James as mentioned in interviews, is the new guy has to be someone they get along with, back stage, on the tour bus, etc. Everyone in DT is married with kids, and that is very important to them, and not being a married with kids type of person was a big part of why Derek Sheridian didn't work out with the band. Also, most of the guys in DT are spiritual/Christain on some level.
For these reasons, I don't see them going with a young or unknown guy. They want someone who's experienced with being on the road, and someone who won't be trying to bring groupies back stage.
So to the candidates:
Mike Mangingi played on the first 3 or 4 James LaBrie solo projects, plus he was with Stvee Vai for a long time, and Petrucci is a big fan of and friends with Vai. He is also an east coast guy, as is most of the band, so that have that in common. He played with Annihilator, so he has the metal cred. I'm not sure if he's married or has kids, but he's at least in a similar age as the rest of the band.
Bobby Jarzombek doesn't have a direct connection, but he has been playing with Fates Warning, and all the guys in DT are good friends with the guys in Fates Warning. He has the technical abilities, and is a metal monster. He's married, I don't know if they have kids.He is the right age. His only con is he's not an East coast guy, but that's not a total deal breaker. Overall, he just fits.
Rod Morgenstein: All of Dream Theater are Dixie Dreg and Steve Morse fans, so they'll familiar with Rod's playing. Jordan Rudness played with Rod in the Dregs, and they have the Rudness-Morgenstein project with several albums under their belt. In addition, Myung has played with Morgenstein in the Platypus and Jelly Jam projects. His only con is he's not exactly the most metal compared to other candidates, and he is also a bit older than everyone else in the band. Thus his chances are a bit less.
A guy I can't leave out:
Jason Rullo of Symphony X. I'm not sure how much he's want to leave his band for DT, but it would be a step up in terms of record sales. He's from Jersey, so he has the east coast thing. He's married with kids. He's the right age. His band is similar enough to DT that he fits the prog-metal criteria Dream Theater would be looking for. And the two bands have toured together here and there, so I'm pretty sure they know each other.
Guys that I don't think quite fit:
Danny Carey isn't leaving Tool for Dream Theater. Tool sells far more records than Dream Theater can even dream about (pardon the bad pun).. Tool just finished a successful US tour, and even though Maynard is currently out with A Perfect Circle, the rumors are strong that Tool is working on a new album. Plus Danny is very into his magical arts and sciences thing, which would be weird with many of the guys in DT being more Christian oriented. But overall, going from Tool to DT would be a step backwards in career moves.
Virgil Donati is great double bass player, but he comes from much more of a jazz and fusion background than a prog-metal background. He could certainly play the material, but I don't him being the kind of guy they really want. And he's bouncing between Australia and Los Angeles, so I'm not really sure how much he and the rest of the band have in common as people, or as in common gigs that gives him an "in".
Thomas Lang, is a technical monster, but the band doesn't just want a technical monster.
He's a bit younger than the rest of the band. Being from Europe and living in Los Angeles, again I'm not sure how much in common he has with the band. I don't rule him out as much as I do Carey or Donati, but still, I'm not seeing it.