Chemistry of both cells are elegantly quoted by forbidden.
Now:
Practicality:
Button cells: inexpensive, portable, used in alot of appliances already
Mercury: more expensive, provides steady voltage (a property desired in watches and pacemakers)
Environmental:
Button: minimal. Alkalinity can cause some concern, but still minimal
Mercury: Mercury is heavy metal, which if is disposed negligently, can cause detrimental effects to environments, such as (well,) mercury poisoning.