An ecosystem is quite smaller than a biome and exists within a biome.
A biome refers to a large habitat ocupied by assorted fauna and flora. Biomes are classified based on abiotic conditions such as temperature, soil types, rainfall etc. An ecosystem is a self supporting unit in which materials and energy are exchanged within the system.
The difference between a biome and an ecosystem is that a biome is a collection of different ecosystems that are found within a habitat while an ecosystem is composed of living and nonliving factors. An ecosystem is quite smaller than a biome and exists within a biome.
