Omni-Channel Routing: Expected routing behavior differences between Chats and other objects

LiveChatTranscript
Chats routed through Omni-Channel will be canceled if no agents are available. Agents considered valid routing targets by the Chat Button configuration (i.e. through Queues or Skills) will be tried no more than once for routing. If that agent declines the chat through push timeout or manual decline, they will not be retried for that chat request. If all available agents are exhausted, the chat request will fail. 
- This behavior is similar to classic routing

Other objects
Other items routed through Omni-Channel will retry existing agents once they exhaust all valid routing targets. For example, a queue-based routing operation may take on this routing path: