I think if you look at the trend over several years the simple answer is Eagle has the quickest progression to a command by a long shot. A couple of blips in Air Nelson/Mt Cook promotion "doth not maketh" them airlines where, generally, commands come quickly. This could be due to the fact that they pay progressively more than Eagle and that some of their pilots are there for the lifestyle. This opposed to Eagle which is often seen as a "stepping stone" to a so called "bigger & better" job (ie jet job).
Even with projected hiring, you'd imagine more would be sucked out of Eagle than the other two.