Both projects are predicated on the core idea that in order to have ETH like programmability/interoperability, applications need to have separate chains, preventing congestion on the overall network.
The difference comes in how they to achieve this. @polkadot's model is that all interactions between separate chains will be intermediated through a "relay chain" via a protocol called XCMP.
$DOT is designed to manage the scarce space on @polkadot. Applications that want to use XCMP must buy $DOT to both rent out a slot on the @polkadot chain and pay fees. Many investors see this value capture as key to the value of $DOT, but it is unlikely to materialize.
The XCMP protocol is still in the specifications phase, where as IBC is complete and will be live on the @cosmoshub in early 2021. This means that @polkadot, as an ecosystem, is at least a year behind from a core technology prospective, as well as having an explicit tax on usage.
With all this in mind, why would a chain pay the $DOT tax when they can use the functioning, permissionless IBC protocol to accomplish the same thing? Here's a hint: they won't, those chains will be using IBC
On top of this core infrastructure and community we have developed and are building the $ATOM2021 roadmap to accelerate value capture for $ATOM. This roadmap has been formulated with the decentralized architecture of IBC in mind from the beginning.
By the time @polkadot chains begin adopting IBC en masse and $DOT is forced to pivot its value capture strategy, it will be too late. They will still be years behind $ATOM, with no hope of catching up.
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A quick thread on the primitives that make up #ibc. There are four major ones: 1. Clients 2. Connections 3. Channels 4. Packets
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In IBC, a "Client" is an instance of a lite client for another chain that is committed to state. This piece is fundamental to the function of #ibc. All other primitives rely on clients to prove their data was included in the counterparty chain.
Once we have a client to prove data, we create a "Connection". This requires 4 transactions, 2 on each chain. The clients are updated throughout to prove the newly committed state on both chains.