If I do compenstate for the light meter by adjusting iso on the d610, then I will be losing quality when compared with the D3300.
You have it backwards. If you adjust ISO manually to
increase exposure on the D610, you are letting in
more light, and thus better quality. But not more light than the D3300; what you should be trying to do is force them to let in the same amount of light for a given scene.
What I'm seeing from your two bodies is that when the exact same manual settings and same lens are used, then you get a similar result.
The D610 meter does appear to be underexposing images, but if you set a global +1 on the exposure compensation you won't have to think about it ever again. Go to custom settings B5 and plug in +1 exposure compensation, then the D610 meter should shoot the same scene on P, S, A, or auto-ISO mode as the D3300 in its current setting. (All of this assumes that the D3300 is the meter that is getting it right. Maybe it's the one that's overexposing instead of vice versa?)
When the D610 and the D3300 shoot the same scene at the same settings, technically the D610's low light performance should be better because the pixels on the sensor are bigger and can take in more light. But, the D610 has an older processor (Exspeed 3 v. D3300's Ex. 4), so maybe the D3300 is rendering the final product better. Also, the image created from the lens is spread out over a larger surface which should allow more detail.
The advantages of a bigger processor are not just low light, but the ability to get better bokeh/shallower depth of field in portraits.