  Massive star evolution is still poorly understood, and observational tests
are required to discriminate between different implementations of physical
phenomenon in stellar evolution codes. By confronting stellar evolution models
with observed properties of blue supergiants, such as pulsations, chemical
composition and position in the Hertzsprung-Russell diagram, we aim at
determining which of the criterion used for convection (Schwarzschild or
Ledoux) is best able to explain the observations. We compute state-of-the-art
stellar evolution models with either the Schwarzschild or the Ledoux criterion
for convection. Models are for $14$ to $35\,M_\odot$ at solar or Large
Magellanic Cloud metallicity. For each model, we compute the pulsation
properties to know when radial modes are excited. We then compare our results
with the position of blue supergiants in the Hertzsprung-Russell diagram, with
their surface chemical composition, and with their variability. Our results at
Large Magellanic Cloud metallicity shows only a slight preference for the
Ledoux criterion over the Schwarzschild one in reproducing at the same time the
observed properties of blue supergiants, even if the Schwarzschild criterion
cannot be excluded at this metallicity. We check that changing the overshoot
parameter at solar metallicity does not improve the situation. We also check
that our models are able to reproduce the position of Galactic blue supergiant
in the flux-weighted-gravity -- luminosity relation. We confirm that overall,
models computed with the Ledoux criterion are slightly better in matching
observations. Our results also support the idea that most Galactic $\alpha$ Cyg
variables are blue supergiants of the group 2, i.e. stars that have been
through a previous red supergiant phase where they have lost large amount of
mass.
