It seems that, although CIELUV and CIELAB were considered equally good when adopted in 1976, CIELAB has generally been preferred more recently (e.g. for the 1994 and 2000 "Delta E" formulae [1]).
In theory, CIELUV is a bit more directly relevant to colored lights or images on a television / computer display, whereas CIELAB is defined for surface colors. In practice, CIELUV just isn’t a very good uniform model of human color vision, and CIELAB is somewhat better (even for display colors) while still being quite easy to compute.
The reason color difference measures are defined with reference to CIELAB coordinates is that they are typically used for specifying tolerances on surface colors in industry. For instance, you might specify that a particular textile or paint color must be within a particular perceptual distance of a target color. CIELUV wouldn’t make any sense for such a use case.
Personally, I’d recommend people move on to use IPT or CIECAM02 or something similar instead.