According to the test results D5200 performed slightly better then the D7100. See also the Nikon D7100 vs d5200 Specs Comparison table here.
Nikon D5200 DSLR Performed Better Then Nikon D7100
Nikon D7100: Update to popular DSLR drops anti-alias filter for sharper images
The new Nikon D7100 is a worthy replacement for the D7000, maintaining its reputation for superior image quality among APS-C-based DSLRs. With an impressive new feature set and the ability to deliver better sharpness and resolution due to the elimination of the anti-aliasing filter from its 24.1-megapixel CMOS sensor, the D7100 takes over as Nikon’s flagship APS-C DSLR. Not only does it maintain Nikon’s position at the top of the APS-C performance charts, but it also gives full-frame competitors a run for their money, delivering similar image quality results for $1,000 less.
The current top 3 best APS-C cameras tested by DxOMark are the Nikon D5200, D7100 and Pentax K-5 IIs