Before we address the question directly, let's talk about the meaning of the Diffraction Limited Aperture.
Diffraction Limited Aperture (DLA) is only applicable at 100% viewing size. This is because DLA assumes a Circle of Confusion (CoC) equal to the pixel pitch of a particular sensor. The effects of diffraction at the DLA are only observable if the resulting image is magnified enough that the viewer can discretely resolve individual pixels. For an 18MP image viewed on a 23" HD (1920x1080) monitor that is the equivalent magnification of a 54"x36" print!
Take for example the 20.2MP full frame Canon 6D and compare it to the 20.2MP APS-C 70D. (I have easier access to the data for Canon gear). Both have the same resolution: 5472x3648.
- The 6D has a pixel pitch of 6.54µm and DLA of f/10.5
- The 70D has a pixel pitch of 4.1µm and DLA of f/6.6
Lets assume a 100mm lens on the 70D and a 160mm lens on the 6D. But then it gets a little tricky, because for a 36mm insect to fill the frame on the 6D (which has a 36x24 mm sensor) you need a 1:1 Maximum Magnification (MM). For the same 36mm insect to fill the frame of the 70D, you would only need an MM of 1:1.6 because the sensor of the 70D is only 22.5mm wide.
At 160mm a 1:1 MM is achieved at a focus distance of 16.8" (MFD
interpolated from the specs for the Canon 180mm Macro lens). At 100mm
a 1:1 MM is achieved at a distance of 12", so a 1:1.6 magnification
would allow a distance of 19.2"
At the 6D's DLA of f/10.5 (the closet Av on the DoF chart I am using
is f/11) using a 160mm lens focused at 16.8", the depth of field is
0.12 inches for an 8X10" print viewed at 10 inches.
At the 70D's DLA of f/6.6 (the closest Av on the DoF chart I am using
is f/6.7) using a 100mm lens focused at 19.2", the depth of field is
0.19 inches for an 8X10" print viewed at 10 inches.
So strictly in terms of diffraction versus depth of field, the shorter lens with the smaller sensor would allow a greater DoF at the DLA for each camera.
This does, however, ignore the effects of noise and noise reduction on the detail present in the final image. The 1.5 stop narrower aperture used by the 6D is less than the 1.8 stop light gathering advantage of the larger sensor (1.6*1.6=2.56 2.56/√2=1.8). But the differences in sensor technology between two cameras from different manufacturers and generations of sensor evolution may well be greater than the very slight advantage here.
It also fails to take into account the differences in the actual shape of the aperture blades of various lenses and their effect on diffraction as well as variables in terms of acutance and other optical qualities between the two different lenses. These may well influence final image quality to a far greater degree than using an aperture beyond the DLA to get the same DoF.
Since you've now modified your question with specific camera/lens combinations we will examine that comparison as well. Some data has been interpolated because we could not find exact specifications published.
- The Nikon D4 has a pixel pitch of 7.2µm and a DLA of f/11.5
- The Olympus OM-D E-M5 has a pixel pitch of 3.7µm and a DLA of f/5.9
- The Tamron SP AF 90mm f/2.8 Di Macro has a 1:1 MM at an MFD of 11.4"
- The Panasonic Leica DG Macro-Elmarit 45mm F2.8 has a 1:1 MM at an MFD of 6"
Due to the 2:1 difference in sensor sizes (linear), the Panasonic lens on the E-M5 would yield a 1:2 magnification at 12"
At the D4's DLA of f/11.5 (f/11 on the chart) using a 90mm lens focused at 11.4", the DoF is 0.19 inches.
At the E-M5's DLA of f/5.9 (f/5.6 on the chart) using a 45mm lens focused at 12", the DoF is 0.26 inches
Again, the (roughly) 2 stop difference in aperture is offset by the (roughly) 2 stop light gathering advantage of the D4 sensor. Note also that since your 36mm bug is occupying the long dimension of the sensor, the 4992 pixel width of the D4 is 7.5% higher resolution than the 4640 pixel width of the E-M5. (The D4 uses a 3:2 aspect ratio, the E-M5 uses a 4:3 aspect ratio)