Since succeeding Gareth Batty as club captain, Burns has overseen a County Championship title in 2018 while scoring more runs than anyone else in Division One and played 14 Test matches following on from his debut in November 2018.
The opener surpassed 10,000 Surrey runs during the 2019 season and has now scored 10,316 runs for the club across all formats.
On the other hand, at just 21, Pope is a more recent addition to the senior squad with his club debut having come in 2016.
Pope's impressive run with Surrey made him receive his first England call-up after just 15 first-class appearances.
He played two Tests against India in August 2018 before returning to the county set-up and earning a recall for the recent New Zealand tour. He now has 3,124 Surrey runs with a first-class average of 71.31.