Upstream tends to make more. For ChemEs, no problem getting into both. For example, the staple job for a ChemE is in refining, which is downstream. However, in upstream you also need process engineers (ChemEs) for free water knockouts, pipeline, dehydrators, etc. etc.
In upstream, ChemEs are more suitable to a production engineering job as opposed to reservoir or drilling, but that is a very, very general statement (lots of exceptions, ifs and buts). Yes, it is possible to do PetE if you're a ChemE, although I agree that if you want to work as a PetE then it's more logical to get a PetE degree.
Quite frankly, there's too many engineering jobs required in the petroleum industry, you'll be okay as long as you actually try to get in the industry.