  We report a sudden reversal in the pressure dependence of Tc in the
iron-based superconductor CsFe2As2, similar to that discovered recently in
KFe2As2 [Tafti et al., Nat. Phys. 9, 349 (2013)]. As in KFe2As2, we observe no
change in the Hall coefficient at the zero temperature limit, again ruling out
a Lifshitz transition across the critical pressure Pc. We interpret the Tc
reversal in the two materials as a phase transition from one pairing state to
another, tuned by pressure, and investigate what parameters control this
transition. Comparing samples of different residual resistivity, we find that a
6-fold increase in impurity scattering does not shift Pc. From a study of X-ray
diffraction on KFe2As2 under pressure, we report the pressure dependence of
lattice constants and As-Fe-As bond angle. The pressure dependence of these
lattice parameters suggests that Pc should be significantly higher in CsFe2As2
than in KFe2As2, but we find on the contrary that Pc is lower in CsFe2As2.
Resistivity measurements under pressure reveal a change of regime across Pc,
suggesting a possible link between inelastic scattering and pairing symmetry.
