  We compare the mass-radius relationship of strange stars obtained in two
theoretical frameworks describing the color-flavor-locking state of dense quark
matter: The semi-empirical MIT model and a self-consistent approach using the
Nambu-Jona-Lasinio (NJL) model. In the simplest MIT model extended to include
pairing, one can make the equation of state stiffer by increasing the gap
parameter so that larger maximum masses for these objects can be reached. In
the NJL model, however, such an effect is not possible. To increase the gap
parameter within the NJL model to values comparable to those considered in the
MIT case, a noticeably increase of the diquark-coupling-constant strength is
needed, but this in turn softens the equation of state producing a lower
maximum star mass. This behaviour is interpreted as signalling the system
crossover at high diquark coupling from a BCS regime to a BEC one, a process
that cannot be reproduced within the simple MIT prescription.
