Really, you want to use a refining company as the bell weather for the upstream production dominated industry. (Major integrated oils are upstream dominated. I work for one on the downstream side and can promise you that upstream dominates in nearly every aspect.)
While far from a perfect model, the two parts are almost counter opposed. On a short time frame, frequently what is good for refining is bad for production. Oil price goes up, it cost the refiners more to buy (bad thing) but oil goes up increases revenue for production (good thing). Only if the finished product prices are pushed up as much or more is it good for both. Similar (but often much more accurate) on falling prices.
What is good for one can often be bad (or neutral) for the other half. But what is bad for one is usally bad for the other in the near term. While certainly not in current favor (ala COP/PSX and MRO/MPC), it is the (somewhat) counter opposed aspect that (used to) be considered as an advantage in oil (and generally) vertical integration.
Both Exxon and Chevron have small but significant chemicals operations that are doing well in the current environment. In the case of Chevron we already know their Chemicals did well because it is a JV with PSX. VLO has none.