The pair on Friday posted first-quarter results that topped Wall Street forecasts as earnings soared. Exxon's net hit $11.4 billion while Chevron earned $6.6 billion and with analysts expecting the strong results to continue this year.

Both have paid down debt incurred during the COVID-19 downturn, have nearly pristine balance sheets and are spending well below their past levels on new exploration and development projects.

The pair have low, net debt-to-capital ratios of about 4%, a fraction of the double-digit ratios of few years ago, and have cut spending on new projects to less than half their income. The result: huge cash reserves, far in excess of what they need for routine operations.

They differ over what to do next, with Wall Street pushing for higher share buybacks and dividends, worried that too much cash could signal a spurt of big-dollar acquisitions.

Exxon CEO Darren Woods says he is happy to see cash balances rise so the company is well-positioned for a cycle downturn.

"The question is obviously when, but that will come," Woods said, after saying he would "expect to see cash balances higher" in times when the markets are on the top end of the cycle.

The CEO noted strong demand for its commodities and did not oppose acquisitions if a deal can lead to higher returns for shareholders.

"It's got to be one where what Exxon Mobil brings to the table actually increases what either company would do independent of one another," he said.

Exxon was sitting on $32.6 billion at the end of the first quarter while Chevron's vault held $15.7 billion, about triple what it needs for operating activity.

But Chevron, which twice bid on rivals, landing Noble Corp for $4.1 billion during the 2020 downturn, expects to reduce some of its cash, said Finance Chief Pierre Breber.

"We don't intend to hold $15-plus billion of cash on our balance sheet," he said, describing too much cash on the books as "economically inefficient for us to hold it, and it is not our cash, it is our shareholders' cash."