The CRJ engine is the GE CF34. It would make sense for DL to do these in house, as there are more of them on-wing between Comair and ASA than any single engine type in the entire DL mainline fleet.
In general in-house work is the way to go as long as the costs can be reasonably controlled. At CHQ we outsourced heavy checks for a while when the ERJ's were new and spent almost as long fixing each plane when it came back as the heavy check took in the first place. Now we have 3 full-time heavy check lines processing 5-6 planes a month and the quality control is excellent.
DL gets a higher quality by doing heavy work in house, because the employees doing the checks have a vested interest in putting out good work. Crappy work in-house means you have to redo it yourself and your profit sharing, bonus, or stock will directly suffer. Crappy contract work means a faster turn around for the contractor on what's likely a fixed-fee project, so they have incentive to be sloppy. The downtime still costs the operator when the plane comes back to straighten it out, thereby ofsetting the savings of using the lousy contractor in the first place..
..CT