  The origin of the X-ray afterglows of gamma-ray bursts has regularly been
debated. We fit both the fireball-shock and millisecond-magnetar models of
gamma-ray bursts to the X-ray data of GRB 130603B and 140903A. We use Bayesian
model selection to answer the question of which model best explains the data.
This is dependent on the maximum allowed non-rotating neutron star mass
$M_{\textrm{TOV}}$, which depends solely on the unknown nuclear equation of
state. We show that the data for GRB140903A favours the millisecond-magnetar
model for all possible equations of state, while the data for GRB130603B
favours the millisecond-magnetar model if $M_{\textrm{TOV}} \gtrsim 2.3
M_{\odot}$. If $M_{\textrm{TOV}} \lesssim 2.3 M_{\odot}$, the data for
GRB130603B supports the fireball-shock model. We discuss implications of this
result in regards to the nuclear equation of state and the prospect of
gravitational-wave emission from newly-born millisecond magnetars.
