Nikon D3400 has a
24.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor and features Expeed 4 processor. On the other hand, Sigma DP2 Quattro has a
20.0MP APS-C (23.5 x 15.7 mm ) sized CMOS (Foveon X3) sensor and features TRUE III engine processor.
Another difference between these two cameras is that Nikon D3400's sensor lacks anti-alias (Low-Pass) filter. Removing anti-alias filter increases the sharpness and level of detail but at the same time, it increases the chance of moiré occurring in certain scenes.
Below you can see the D3400 and DP2 Quattro sensor size comparison.
Nikon D3400 and Sigma DP2 Quattro have almost the same sensor size, so neither of them has any significant advantage over the other in terms of providing control over depth of field when used with the same focal length and aperture.