Say if I am changing from CoPay to Bitcoin Core, is it recommended that I try and import my CoPay's private keys to Core, or just send the coins over to my Core account.
It depends on two factors.
One is, how many unspents are your funds spread across in CoPay? Will it be a really large transaction which will need high a transaction fee? Then sending to Core might be easy, but at a financial cost.
Two is, how comfortable do you feel with exporting CoPay's priv keys, safely transferring and importing then into Core? If you are OK with it, then you save the transaction fees.