This is a great question. I’ll interpret it below 
- How do Polkadot and Cosmos differ in the developer compositional environment they offer to users/developers?
Polkadot:: Polkadot is essentially operating under the sharding paradigm of interchain interactions. Because effectively the entire network is one unified state machine. The designers of a chain can expose arbitrary apis that other chains can call. One can expect that standards will emerge allowing common patterns like interchain transfers of tokens but developers can freely invented their own mechanisms for interchain interaction.
Cosmos: Because Cosmos is a network of potentially faulty state machines rather than one unified state machine, Cosmos will support sending proof carrying objects between chains rather than arbitrary chain to chain function calls. We are planning a major communication push around our compositional model for Q1 2019 but so I’ll be brief here. Initially, Cosmos will support sending static objects between chains and objects with 1 mutable parameter(their owner). This is sufficient to implement compositional patterns like Summa’s cross chain auctions or transfers of tokens between chains. I’ve long been interested in research on languages that can express more complex relationship between proofs and mutations of complex objects like Agoric’s Jessie and Kadena’s Pact and I expect that something in that domain can express virtually any financial primitive within the constraints of Cosmos. By embracing these constraints, Cosmos provides unlimited flexibility for developer designing their Blockchain state machines, a limitless ecosystem and total freedom to experiment with mechanism design.