Lithium Iron Phosphate batteries are less expensive because they don't use nickel and cobalt. Some do use manganese. The big plus is longer life -- thousands of charge/discharge cycles --- and can be fully charged/discharged without degradation. The downside is less capacity for their weight.

Lithium Ternary batteries use more expensive metals but offer greater capacity for their weight. Besides the higher cost they have a much lower cycle life which is further downgraded but charging them to 100%.

This said, battery technology is changing very rapidly.