In addition to better privacy as mentioned above, running your own node also means you don't have to trust a third party. You can validate all blocks yourself, and you can verify every transaction you send or receive yourself. Any other wallet is connecting to someone else's node and trusting that they are honestly verifying transactions and sending you the correct information.
Another feature you will get is a better manipulation for your coins, you can build your own transactions selecting the inputs you want to choose and spend to multiple addys on the same transaction.
True, but this isn't unique to Bitcoin Core by any means. Most good lightweight/SPV desktop wallets allow coin control and send-to-many.