For small or poorly scattering systems or with low concentrations then the glass cuvettes will always provide better optical quality for size measurement. Zeta potential is measured with a disposable cuvette usually though there are other options such as the dip cell. See attached.
In principle, the type of cuvette should not affect the measurement, and you could convince yourself of the fact by performing a measurement of a known standard in both cuvettes. However, as Alan stated above, for poorly scattering (low concentration or small particles/molecules) samples or those with very low electrophoretic mobility, a glass/quartz cuvette may give you better repeatability (and the dip cell also has a larger electric field strength, as required for example for non-aqueous measurements).