Take a look at the private keys from your Bitcoin Core client. They should look like mine (the following are keys from the testnet):
Now go to your Electrum and take a look at your keys there (Wallet>>Private keys>>Export, you will find them to the right from your addresses). The should look more or less like mine:
They look like of a different type than the ones from your Bitcoin Core wallet.
A single private key can lead to different addresses, depending on the script it is used in - these include p2pkh, p2wpkh, p2sh-p2wpkh. To realize that it is true create a new wallet in Electrum (File>>New/Restore>>Create..,choose option Import Bitcoin addresses or private keys) paste the unprepended private key from your Bitcoin Core wallet. Electrum should create a new non-HD wallet for you with only one address. This adrress will be a different one from the one from which you derrived your private key in Bitcoin Core client
Electrum prepends the script type to the private key during export and import so that it knows which address to derive and check for outputs on.
Before sweeping prepend the private key from your Bitcoin Core wallet, that you got from the output of
dumpprivkey "address", with
p2wpkh:, like so:
p2wpkh:cNbxok3SkFuSsbiiTqLj56Hp6bAhr2uJtr8aTkViBB3ghBMzQH3Y. Such prepended key paste into the sweep box and follow the instructions. You can replace the address given to you by Electrum with the one of your choice - it will work as well.
What is convenient in sweeping is that it will work even if you do not have any Bitcoin in your destination wallet. The fee will be taken from the source, in your case the UTXO from the address of your Bitcoin Core client.