For the former, essentially you're dealing with multiplying lower chance of death with much higher infection rate, resulting in bigger count of deaths (and other events like hospitalisations, isolation, etc., which increase economic disruption).
Once you jump it back to humans it's a new roll of the dice on whether it's more or less deadly and infectious.
We're going to deal with long history of disablement caused by how COVID attacks neural tissue, for example, something I think might be more disastrous long term (1918 flu was similar, with some historic effects like Aktion T-4)
But, also this: https://twitter.com/andrew_croxford/status/14762098046666014...
Ah, and I see the tweet is trying to dispel fear that was worked up around this. Got it.
Reasonable starting point for looking further:
A better argument against it would be that there is a huge unknown, and the very uncertainty about something which cannot be undone, is a reason not to do it.
Besides the "short term overload" aspect, this doesn't have much weight if both viruses ultimately end up infecting the majority of the population.