Babylon consists of two main parts: the Bitcoin timestamp protocol and the staking protocol. It operates on its own chain built using the Cosmos SDK, featuring its verification nodes and independent components like the EOTS Manager and Finality Provider.
EigenLayer, in contrast, is primarily a set of smart contracts operating on the Ethereum network, handling user stakes and managing AVS contracts. Ethereum's support for smart contracts allows EigenLayer to implement more complex slashing conditions.