Republic seems to have a lock on the E170, which is the preferred aircraft for outsourcing mainline flying. SkyWest has the CRJ700 (and derivative AC), which are marginally more efficient, but less service transparent.
When you consider how far Republic has come since it began in 1996 it is a pretty amazing company. I certainly did not expect it to do so well. For any Delta Connection pilot this route map is pretty scary:
http://www.republicairways.com/images/destinations/maps.pdf
We still don't know how the Delta Connection RFP will shake out (and probably will not until Comair and ASA pilots have been whipsawed to Delta and SkyWest's maximum gain) but my bet is that more E170 and CRJ700 flying will be in the cards.
At both carriers there is a possibility that 50 seat aircraft will go away. At SkyWest, you would be insulated by the fact that 50 seat cuts will probably hit ASA first since 40 aircraft are linked to Delta's bankruptcy and could be flipped back to leaseholders without much drama.
It is a difficult call, but I'm up this morning doing research on buying RAH stock. (With the US Air consolidation threat gone there should be upside potential for SkyWest and RAH.)
In other posts, RAH has opined about hiring 1,000 pilots. That would probably put you in the left seat. SkyWest was hiring 80 a month. Your upgrade chances are almost always better at a smaller carrier that is has good growth potential.
All things considered amongst these two good choices, I think RAH is the better choice.