With the weak results and Chevron's shares down nearly 24 percent this year, Stewart Glickman of S&P Capital IQ downgraded the stock to "hold" from "buy" on Friday.
"We're in what looks to be a sustained low oil price environment, and in that kind of environment I would rather be playing defense," Glickman said Monday in a CNBC "Power Lunch" interview.
Read MoreChevron posts worst profit in nearly 13 years
He contended that owning Exxon Mobil shares could protect investors playing the oil space. He upgraded the stock to a "buy" from a "hold" on Friday.
Exxon's advantage over Chevron lies in its free cash flow, which allows it to drive value by returning money to shareholders even if prices remain low, he said.
Still, Exxon has suffered amid the crude meltdown. Its second-quarter profit, reported last week, tumbled more than 50 percent from the year-earlier period.
Read MoreExxon Mobil posts earnings of $1.00 a share vs $1.11 expected
Exxon shares have fallen more than 15 percent this year.