Occidental Petroleum CEO Vicki Hollub said Wednesday her company can squeeze the best results out of Anadarko Petroleum's wells in the top U.S. shale basin, making Occidental a better acquirer than Chevron.

Earlier Wednesday, Occidental launched a rival bid for Anadarko, which agreed to sell its business to Chevron in a deal valued at $33 billion earlier this month. Occidental is offering $76 a share for Anadarko, representing a roughly 20% premium to Chevron's $65-per-share offer.

Hollub says 75 percent of Anadarko's value lies in its assets in the Permian Basin, the shale oil region underlying western Texas and eastern New Mexico. The Permian is the epicenter of a boom in U.S. oil production.

"We are the right acquirer for Anadarko Petroleum because we can get the most out of the shale," Hollub told David Faber on CNBC's "Squawk Box." "We have a lot more experience there. We are performing really, really well, and what hasn't been talked about very much is that the upside in this deal is the shale play, is the shale development."

Shares of Occidental fell about half a percent on Wednesday, while Chevron's stock price slumped 3.1%. Meanwhile, Anadarko shares surged 11.6% for the biggest daily gain in the stock index.

Anadarko confirmed on Wednesday that it had received Occidental's unsolicited bid. The company said its board will carefully review the proposal to determine the best course of action for shareholders.

"The Anadarko board has not made any determination as to whether Occidental's proposal constitutes, or could reasonably be expected to result in, a superior proposal under the terms of the Chevron Merger Agreement," the Company said in a statement.

Chevron is also pitching itself as an ideal steward of Anadarko's Permian assets. The oil major says the deal stitches together a 75-mile-wide strip of continuous land in the Delaware Basin, a sweet spot within the larger Permian. That allows Chevron to bring efficient, industrial-scale production to the shale field, the company says.

"We are confident the transaction agreed to by Chevron and Anadarko will be completed," said Kent Robertson, manager for global external affairs for Chevron.