Citi Research analyst Mark May swapped his stance on the big online-travel players on Thursday, upgrading Booking Holdings Inc. shares to buy from neutral while downgrading Expedia Group Inc. shares to neutral from buy. May sees stabilization in room-night trends for Booking, formerly known as Priceline, as well as encouraging data around European and Latin American travel trends. "Booking has significantly upped its buybacks of late, and we believe that trend will continue and potentially increase further (we forecast as much as a 13% shrink between 1Q19 and YE20)," he wrote. On Expedia, May is concerned about the company's alternative-rental business, which is now called Vrbo. "Vrbo's growth has disappointed and slowed meaningfully, and this could persist (and weigh on Expedia's overall growth) given Vrbo changes, Google changes, and heightened competition," he wrote. May increased his Booking target price to $2,100 from $1,800 and lowered his Expedia target to $130 from $145. Booking shares have ticked up 1.3% so far this year, as Expedia shares have risen 3.6% and the S&P 500 has increased 14%.