Canon SX510 HS has a
12.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CMOS sensor and features Digic 4 processor. On the other hand, Canon SX600 HS has a
16.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features DIGIC 4+ processor.
Below you can see the SX510 HS and SX600 HS sensor size comparison.
Canon SX510 HS and Canon SX600 HS have the same sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture.