Is there any advantage to incubating an egg with the infinite use incubator, or the limited uses incubators? Are CP values or rarity of the hatched pokemon affected by the type of incubator used?
There is no difference between hatching with each incubator.
However, if you want to get the most out of your temporary incubators, it is recommended that you try to only hatch 10km or 5km eggs in the temporary ones (preferring 10km). Doing this will allow you to be hatching more eggs at a time.