  Nuclear matrix elements (NME) are a crucial input for the interpretation of
neutrinoless double beta decay data. We consider a representative set of recent
NME calculations from different methods and investigate the impact on the
present bound on the effective Majorana mass $m_{\beta\beta}$ by performing a
combined analysis of the available data as well as on the sensitivity reach of
future projects. A crucial role is played by the recently discovered
short-range contribution to the NME, induced by light Majorana neutrino masses.
Depending on the NME model and the relative sign of the long- and short-range
contributions, the current $3\sigma$ bound can change between $m_{\beta\beta} <
40$ meV and 600 meV. The sign-uncertainty may either boost the sensitivity of
next-generation experiments beyond the region for $m_{\beta\beta}$ predicted
for inverted mass ordering or prevent even advanced setups to reach this
region. Furthermore, we study the possibility to distinguish between different
NME calculations by assuming a positive signal and by combining measurements
from different isotopes. Such a discrimination will be impossible if the
relative sign of the long- and short-range contribution remains unknown, but
can become feasible if $m_{\beta\beta} \gtrsim 40$ meV and if the relative sign
is known to be positive. Sensitivities will be dominated by the advanced
$^{76}$Ge and $^{136}$Xe setups assumed here, but NME model-discrimination
improves if data from a third isotope is added, e.g., from $^{130}$Te or
$^{100}$Mo.
