Laser is cheaper. Both will cost a good deal of money. Both are painful in their own ways. Laser may or may not work, depending on you specifically. Ask a laser specialist for an evaluation. They should tell you if you are a good or bad candidate for laser after they examine you. (Dark hair and light skin complexion are the absolute best combinations for laser.)
Electrolysis is guaranteed, takes longer, goes hair by hair, is more expensive.
Both can take months to a few years to complete because facial hair grows in waves over time.