REM will always be an ERC20 token and it doesn't support swapping to EOSIO. However, after mainnet REM have its own mainnet token which can be swapped between the two chains (Ethereum and REMChain) through atomic swaps. If you intend to use services on REMChain such as being a BP or a Guardian of the network, then you will need to swap your REM (ERC20) into REM (REMChain). If you are planning to trade it on exchanges then its better left as an ERC20.
What's next: REM ERC20 and REMChain native tokens