A slew of integrated energy majors are reporting earnings, and while the familiar theme is that downstream operations, specifically refining, are weak and will be weak for some time, notable contrasts are emerging. Supermajors like Chevron (NYSE:CVX) and ExxonMobil (NYSE:XOM) have similar business structures and equally impressive operational reach that extends across the globe, but their results indicate differences in their performance.

You might be questioning whether you should give Chevron and ExxonMobil the benefit of the doubt and ride out the storms. While Chevron and Exxon are still immensely profitable, well-run businesses, the headwinds facing downstream profits can't be ignored. As a result, while you might stick with Chevron or Exxon, here's why a better candidate may exist among big oil.

One major headwind going forward
The one huge weight dragging down big oil profits continues to be downstream, and more specifically, refining activities. There's simply no way to get around the fact that as long as spreads continue to contract, margins will continue to compress, and downstream profits will suffer. That being said, Chevron deserves credit for navigating the tough downstream climate better than some of its rivals.

Chevron's U.S. and international downstream segments generated $380 million in earnings, down 55% from $689 million in the same quarter last year. By comparison, ExxonMobil's downstream earnings fell a whopping 81% in its most-recent quarter, year over year.

In all, Chevron's net income clocked in at $5 billion in the quarter, down nearly 6% from the same period last year. Boosting Chevron's bottom line continues to be solid upstream results, driven by increased production. Furthermore, project ramp-ups in the United States, Nigeria, and Angola will serve as a catalyst for further growth in the company's upstream segment.

While falling profits should rarely be celebrated, Chevron is holding up much better than its closest U.S. peer, ExxonMobil. ExxonMobil's quarterly profit fell 18%, primarily because it leans on refining to a larger extent than Chevron.

Should you endure the muddle-through period?
It's no secret that integrated energy majors are suffering due to the intense downward pressure on refining activities. Upstream operations continue to perform well for Chevron and ExxonMobil, but there's only so much these companies can do when their downstream activities are posting huge profit decreases.

As I see it, you have two options in light of the horrible refining climate: stick it out, or choose a major that isn't heavily reliant on refining. For those interested in the latter, I'd suggest ConocoPhillips (NYSE:COP), which is less integrated than its peers because it spun-off its refining unit last year. As a result, Conoco's underlying results have looked much better in recent quarters.

Consider that Conoco's third-quarter earnings increased 7% year over year, thanks to growth in its higher-margin businesses such as U.S. and Canadian liquids. In addition, margins expanded during the quarter: Conoco realized an average price per barrel of oil equivalents of $69.68 in the third quarter, up from $65.62 per barrel in the same quarter last year.

If you stick with Chevron and ExxonMobil, you'll continue to receive healthy dividends that beat the yield of the broader market. Whereas the S&P 500 pays about 2% and a 10-year Treasury Bond yields just 2.6%, Chevron and ExxonMobil pay 3.4% and 2.9%, respectively. Of course, if dividends are what you're after, ConocoPhillips beats them all, with a 3.8% payout.

Final thoughts
As a result, while Chevron and ExxonMobil are two highly profitable blue-chips, there's no escaping an extremely poor refining environment. They're both going to emerge from these tough times unscathed, but when is uncertain. For the time being, ConocoPhillips provides shelter against refining dragging down profits. And, Conoco offers a higher dividend than either Chevron or ExxonMobil and, consequently, may be the best choice among the three.