Hi Sarah from Open Privacy / Cwtch team here - the main major difference is that Cwtch servers are completely untrusted under the risk model - they don't learn anything about the groups they are hosting, who is a member of which group, or who each message is for.
Metadata resistant group comms is still a fairly large open research problem, and we are also working on the research side to reduce some of the bandwidth requirements that are currently required by our group protocol: https://git.openprivacy.ca/openprivacy/niwl
On Android we implement a background service that will wake up periodically and either use the active tor connection or start a new one if the kernel has stopped it for any reason - and also reconnects the UI. This makes Cwtch connections fairly stable on android devices - even for p2p.
However, it also means that Cwtch on Android is fairly battery intensive. We provide a way to easily shutdown Cwtch completely for this reason - and we are researching ways to minimize power consumption (both through tor optimizations and alternative anonymous communication networks)