RE: Is Dogecoin more popular than Bitcoin Cash?
It is clear there is more interest. It's less strong evidence of commerce (other than speculation), because tokens which clearly have no commerce on their blockchain still have a lot of money sloshing around on exchanges.
Median transaction value is itself something easily manipulated on chain. The cost of creating transactions if you send to yourself is not related to the value of the transaction but the physical size in bytes. Median transaction value would also be expected to decline over time with real commerce, because in real world commerce there are vastly more small-value transactions than large ones. Since the median for Dogecoin is $36, it wouldn't be unexpected for Bitcoin Cash to go below that if it were doing large amounts of real world commercial transactions.
The median and average can't prove commerce use of course, but it also doesn't disprove it. I'm not aware how much commercial use there actually is of Dogecoin, but I know of some businesses that only accept Bitcoin Cash.
Something like BitPay and Coinbase coming out and detailing their merchant trade volume in each of the currencies they facilitate would be the best possible evidence.
Dogecoin used to do loads of transactions via the Reddit tip bot. The first one is now defunct (was running a fractional reserve and lost everyone's money), the second one does barely any transactions these days:
https://www.reddit.com/user/sodogetip
There are other doge tip bots on Twitter and other platforms but they're not doing loads of transactions as far as I'm aware today.
Dogecoin actually used to have pretty good merchant adoption compared to most cryptos, but that was several years ago. If you go through this page now they are largely defunct or inactive:
https://www.dogecoins.com/spend.php
In the absence of evidence of any significant activity, I think it's fair to assume the Dogecoin transactions are mostly self-transfer spam.