Sony A77 has a
24.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor and features Bionz processor. On the other hand, Nikon D780 has a
25.0MP Full frame (35.9 x 23.9 mm ) sized BSI-CMOS sensor and features Expeed 6 processor.
Below you can see the A77 and D780 sensor size comparison.
As seen above, Nikon D780 has a 2.3x Larger sensor area than Sony A77. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in same focal length and aperture.