Media with different formulations were created for different purposes. Sometimes small differences in components can have a big effect on the growth and function of cells. So, in general, do not switch media.
It is likely that sensitive cells, like stem cells, will not react well to a sudden change in media, but it depends on exactly what stem cells you are using and what you are trying to do with them.
Though high-glucose DMEM is the conventional basal medium for stem cells, it could encourage differentiation. You can use DMEM: F12 (DMEM/F-12 is a 1:1 mixture of DMEM and Ham's F-12) which can support greater growth rates. DMEM and F12 are often mixed to combine the higher concentrations of components in DMEM with the wider range of Ham’s F12 ingredients. For instance, the addition of Ham’s F12 provides components such as biotin, putrescine, lipoic acid, proline, copper, and zinc that are not present in DMEM.
DMEM/F-12 contains no proteins, lipids, or growth factors. Therefore, DMEM/F-12 may require supplementation, commonly with 10% FBS.
You can refer to the research article attached for more details.
Article Basal medium composition and serum or serum replacement conc...