The transaction fees should be the same regardless of where the transaction is taking place, but you can change the price of the transaction in order to get it pushed through blockchain faster. Exchanges do have additional charges on top of that, and they fluctuate depending on the exchange.

I wasn't sending my friend to Coinbase because the transaction fees were cheaper, but sending them to Coinbase because they could get Bitcoin and store it in the Coinbase wallet and (I believe) not have to deal with any transaction fees if they left it stored in the Coinbase wallet.