Both Nikon D5200 and Nikon D3400 have APS-C sized 24.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
One other difference between these two cameras that is worth mentioning is that Nikon D3400's sensor doesn't have an 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 D5200 and D3400 sensor size comparison.
Sensor Size and Resolution Comparison image of Nikon D5200 and Nikon D3400 Cameras
Nikon D5200 and Nikon D3400 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.
DxOMark Sensor Scores
DxOMark is a benchmark that scientifically assesses image quality of camera sensors. It scores camera sensors for color depth (DXO Portrait), dynamic range (DXO Landscape) and low-light sensitivity (DXO Sports), and also gives them an overall score. Nikon D5200 and Nikon D3400 sensors have been tested by DxO and the results show that D3400 has a better overall score of 86, 2 points higher compared to D5200's score of 84.
Model
Overall
Color Depth
Dynamic Range
Low-light ISO
Nikon D5200
84
24.2 bits
13.9 Evs
1284 ISO
Nikon D3400
86
24.8 bits
13.9 Evs
1192 ISO
Sensor size sets the circle of confusion, so it drives how much depth of field each
of these bodies gives you at a given aperture. You can calculate it exactly for the
Nikon D5200
or the
Nikon D3400 ,
including hyperfocal distance.