In general, no, it costs the same. But it may differ if there is some special logic when transferring the tokens.
In the case of Ethers, it will always be the same if the receiver is an EOA (Externally Owned Account, a wallet), since there can't be any logic at the receiving end. If the receiver is a contract, it may start some special processing which may run different parts of the code depending on the amount of Ether sent. In that case the gas cost is different.
In the case of tokens, it doesn't matter who the receiver is, since there is always code which is executed. So there may always be special processing depending on the transferred amount.