Neither of those even with millions of users (and especially if you expect them to be on mobile) will be sufficient to secure the chain against powerful attackers such as botnets with gaming rigs and hijacked Amazon EC2 or other VPS cloud accounts.
Thank you for your quick answer and the references. That's a valid objection from a practical point of view. I'm not sure to what extent using the
cumulative hashing power contained in the (meta) blockchain could help in that respect:
https://bitcointalk.org/index.php?topic=1570198.msg15972492#msg15972492.
In such a setting you would probably need to run your botnet for months or years in order to build a longer chain (of the transactional blockchain).
This is certainly more risky and costly than renting the computing power for some hours to build an alternative chain in traditional PoW currencies.
How did you solve this issue in your version of unprofitable PoW?