When you compare schools with similarly high levels of poverty, the gap between rural and urban academic performance is much smaller, and some studies find little or no difference in test performance.
A particularly clear NCES analysis looked at 10th-graders and divided schools by both location and poverty concentration. Among schools where more than 40% of students were from low-income households, the average achievement score was about 45 in urban, rural, and suburban schools. The study concluded that urban high-poverty students performed no differently from students in high-poverty rural schools on that achievement measure.