There will be minimal difference; particularly for macro type photography where the aperture generally has to be stopped down in order to achieve a usable depth of field.

The D610 has a pixel size of 5.95um and the D810 has a pixel size of 4.87um. In order to resolve all visible light wavelengths to that size requires a (theoretical) perfect lens used at f/2.8 (red 4.8um, green 3.8um, blue 2.7um). At f/4 the same lens would project red light at 6.8um in diameter. And at f/8 even the blue wavelengths would be at 7.8um. But we can safely assume that the lens in use is not perfect, and the results will be at least one stop worse.

When the size of the airy disk exceeds the size of the pixel contrast is reduced. Whereas smaller details require greater contrast in order to be discernible. And when the airy disk becomes significantly larger than the pixel (2x), recorded resolution decreases.

If I use DXO's measurements of a very good long macro lens such as the Sigma 150mm, it shows that the lens is sharpest at f/4 and delivers 18MP on the D610 and 23MP on the D810 when at f/4. By f/11 it is near 12MP on both sensors. The higher resolution sensor always gives some small gain in recorded resolution due to oversampling, but it is seldom anywhere near what the specs would indicate.

But you are also indicating that you don't actually need much recorded resolution at all. The attached image is less than 0.41MP in resolution, and the amount of detail it contains is significantly less than that.

In this scenario a camera of even less resolution like a 12MP D3 might actually be more beneficial due to it's much larger pixel size (8.4um)... However, another consideration is that only the D810 does not have an AA filter which gives it another potential advantage. And when operating with settings/situations that do not allow you to maximize the D810's resolution, the recoded images are still not any worse. That's why I own/use a D850, even though I seldom actually benefit from it significantly.

https://www2.uned.es/personal/rosuna/resources/photography/Diffraction/Do%20sensors%20outresolve.pdf

EDIT: Based upon the added information of camera/method used, I would say your main issue is lighting and shutter speed, or rather, shutter speed which better lighting will help with. When working with longer SS's there are many things that can contribute to a lack of sharpness... mirror slap, floor vibrations, etc. And even if you mitigate all of those things you are still going to have an issue.

That's because there is a current in the aquarium... the corals require it to survive. And the current causes movement in the subject; even if it doesn't cause movement in the subject it can cause minor changes in the diffraction/focus as the water moves between the lens/subject.

My best suggestions to improve your results: Make certain the lens axis is exactly perpendicular to the glass face of the tank. Get the SS up to at least 1/250 if at all possible (or use off camera flash). Turn off the current/pumps if possible.

The pumps and SS are somewhat reciprocal; you can probably get away with a lower SS w/ the current/pumps turned off. But the first point is pretty critical... I suspect a lot of your noise/blur is actually due to off axis diffraction.