Concrete is a common fix where floor joists have rotted (usually due to blocked air bricks or rubble in the subfloor). Best do both rooms or neither, just doing 1 will deprive the other of airflow. And don't be lazy (like the clowns who concreted floors in my House of Pain and left the joists in).
Pro:
Easy to insulate - lose all the timber, chuck hardcore, sand, dpm, insulation boards, concrete in the hole.
No air bricks needed (so no draughts behind the skirting boards)
Quieter.
No risk of joists rotting.
Con.
Need to duct or reroute heating pipes, power cables, comms cables etc.
Need to consider gas pipes (if your meter is under the stairs you musn't bury the supply pipe as well as not burying your distribution pipes)
Same with electrical supply (if the meter is under stairs or inside somewhere, don't bury the supply cable).
And water supply.
You'll have to cover the concrete with something (carpet, laminate, timber)- you can finish concrete flat & level but its more common to screed (but more time & money).
EDIT If the floorboards & joists are in good nick you don't have to replace them. Consider insulating between joists while the place is empty, also check you still have airflow now you've concreted the kitchen