On Friday morning, the Dow Jones Industrials (^DJI 0.62%) climbed at the opening bell to set themselves up for another potential record run. But by 11 a.m. EDT, the index had given up that gain and was down 26 points. Most economists focused on a strong jobs report, which showed the U.S. economy produced a 288,000-job rise in nonfarm payrolls in April and the unemployment rate fell to 6.3%, its lowest rate in nearly six years. Among the Dow's energy giants, even though it was Chevron's (CVX 0.21%) turn to report quarterly earnings this morning, rival ExxonMobil (XOM 0.02%) proved to be a much bigger winner in today's trading.

Chevron posted minimal gains in early trading Friday, despite reporting financials that provided further disappointment to investors who were already bracing for poor results. In the Chevron first-quarter earnings report, the oil giant noted drops both in production volume and in crude-oil prices, pushing net income down 27% on a 6% drop in revenue. Like ExxonMobil, Chevron benefited somewhat from the recovery in U.S. natural-gas prices that rose by more than half from year-ago levels. Chevron's downstream segment actually boosted earnings by just over 1%, with its domestic downstream business tripling net income from the year-ago quarter.

But ExxonMobil jumped 1% today after announcing its own results yesterday morning. Investors remain pleased that the oil giant is continuing to count on being able to drill in the Arctic Ocean off the northern coast of Russia, despite the rising threat of new U.S. economic sanctions against Moscow that could jeopardize Exxon's investment in the region. Given the amount of potential production at stake, Exxon desperately needs success in Russia in order to keep its own overall production levels up. Yet ExxonMobil has arguably benefited more from the resurgence in natural-gas prices, especially if its ill-timed acquisition of XTO Energy four years ago finally starts to look more lucrative.

In general, ExxonMobil and Chevron have taken turns rising and falling in investors' eyes, with Chevron's somewhat smaller size giving it a bit more flexibility to pursue opportunities more quickly than its larger rival. Nevertheless, in the long run, conditions in the energy industry will likely keep both ExxonMobil and Chevron moving in the same direction, and both companies are working hard to ensure that the direction they'll go remains upward.