Chevron Corp. (CVX - Get Report) posted stronger-than-expected first quarter earnings Friday, in sharp contrast to its larger rival ExxonMobil Corp.   (XOM - Get Report) , as the company navigates a potential bidding war for independent drilling group Anadarko Petroleum (APC) .

Chevron said earnings for the three months ending in March came in at $1.39 per share, down 26.9% from the same period last year but firmly ahead of the consensus forecast of $1.33 per share. Group revenues were pegged at $35.2 billion, down modestly from last year but missing the Street consensus of $38.42 billion.

"Upstream production volumes were up 7 percent from a year ago, primarily in the Permian Basin and at Wheatstone in Australia," said CEO Michael Wirth. "The company's net oil-equivalent production exceeded 3 million barrels per day for the second quarter in a row. First quarter earnings declined from a year ago, largely due to lower crude oil prices and weaker downstream and chemicals margins." 

"We continue to high-grade our portfolio," Wirth added. "In the first quarter we sold our interests in the Rosebank field in the United Kingdom and the Frade field in Brazil. In early April we concluded the sale of our upstream interests in Denmark."

Chevron shares were marked 0.1% lower at the start of trading Friday following the earnings release to change hands at $117.78.

Exxon shares were marked 2.44% lower at $80.35 each after it posted much softer-than-expected first quarter earnings Friday as weaker industry margins, thanks in part to high U.S. gasoline inventories, hit its bottom line.

Exxon said earnings for the three months ending in March came in at 55 cents per share, down 49.5% from the same period last year and well shy of the Street consensus forecast of 70 cents per share. Group revenues, Exxon said, fell 6.7% to $63.625 billion and against missed analysts' estimates of $67.35 billion.

Earlier this week, Occidental Petroleum (OXY - Get Report) made a formal proposal to buy Anadarko in a deal that would value the independent oil producer at $57 billion and trump a pending takeover proposal from Chevron.

Occidental said it would pay $76 for each Anadarko share, with a combination of $38 in cash and 0.6094 Occidental shares, a price is says represents a 20% premium to the group's pending deal with Chevron. Occidental said its deal would improve free cash flow by $3.5 billion, via cost reductions and synergies, and is superior to Chevron's in both financial and strategic terms.