To your claim:
“The Catholics, OTOH, claim that they are “other Christs” here on earth”
That sounds more like something your Church taugth you about what Catholic’s believe which 99% of the time is nothing but something that has been made up.
May want to go check with headquarters, chris. This is RCC doctrine that no one around here would care to make up, even if they could. Those of us outside of the Roman organization continuously point out these errors with the intention of informing those willing and able to listen. Run, don't walk from Rome.