We have performed lattice resolved annular dark-field (Z-contrast) scanning transmission electron microscopy and combined this with energy-dispersive X-ray spectroscopy as well as simulations to measure quantitatively segregation across strained interfaces in AlGaN/GaN and GaN/InGaN multiple quantum wells of nominal thicknesses between 8 and 0.25 nm. The compositional profiles obtained were corrected for detector dark current and non-linearity of the Z-contrast imaging process before we fitted exponential functions to the profiles across the interface regions. From these, we could highly accurately determine the layer widths, interface widths, and segregation lengths. Experimental values of the segregation lengths calculated varied from 0.3 nm (for InGaN-on-GaN) to 1.4 nm (for AlGaN-on-GaN), with error bars of only +/- 0.05 nm. A comparison with simulations based on a simple two-state-exchange model for surface segregation shows that the segregation energy for indium atoms is about an order of magnitude smaller than both the corresponding segregation energy for aluminium/gallium atoms and the activation energies for surface segregation of cations in these nitride systems.