No you don't fly both types and recruitment is according to experience and needs for each fleet. Large demand for pilots on all fleets but training capacity lacking on Boeing fleets, expect hold pool 12 months plus, Airbus not so long. Qatar want large numbers in hold pool as guys change their minds and circumstances. Some experienced FOs close to upgrade whom passed assessments remaining with current employers, good choice given how the industry changes. Recruitment requirement to be " currently flying" also snow balled some guys out.