What I mean is the following. Imagine two smooth massive spherical bodies ($M_1\neq{M_2}$), with equal and homogeneous mass densities. Both masses have a layer of water on them for which holds ($R_1$ and $R_2$ are the radii of the masses):
$$\frac{R_1}{R_2}=\frac{{{waterlevel}_1}}{{{waterlevel}_2}}$$
The two masses rotate around each other. Their rotations around their rotation axes are the same: $\omega (\frac{rad}{sec})$. The rotation (pseudo)vectors are perpendicular to the plane in which both bodies revolve around each other. Finally, let's assume for simplicity that their orbits are circular.
My question: Will the tides on both bodies be scale independent? Which is to say, can we see any difference in the tides if (in the very hypothetical case) our bodies had the size "fitting" to the planets, by which I mean that if we were shrunk or blown up so it would seem to us that both planets had the same size?
It's my guess that no difference would be seen as both masses of water on the planets would fall at the same rate towards the other, resulting in (relatively) the same tides. Which implies scale invariance.