Dry batteries are maintanance free they do not require topping up like regular wet batteries, and have gel electrolyte
They are basically used in:
(i)aeroplanes since aeroplanes can turn upside down when doing a somersault in the air
(i)roadside cabinets to power up UPSs such as those for cable TV networks etc, since wet batteries would release fumes inside the cabinet which has to be completely sealed to prevent vandalism
For cars the engine cavity has plenty of ventilation so there is no problem of vapors,
Performance wise dry batteries have slightly longer life and thus cost more
Starting a manual car is simple as explained by @humangenius and @takko 