The advantage of after-tax 401k contributions is that they still grow tax free each year.
Remember that investments are normally taxed three different ways: on the way in, as they grow, and on the way you. You pay income tax when you earn the money in the first place (unless you put it in a pre-tax account like a 401k). If you were to invest in a taxable account, you would then pay taxes on the earnings and dividends each year. Then you pay capital gains (or worse yet, regular income tax) when you sell the investment.
So if your alternatives for those dollars are a taxable brokerage account or an after-tax 401k contribution, the 401k contribution still offers you protection from the 2nd of those three taxing possibilities and the taxable account would not.
A Roth IRA would offer you no up front tax deduction, but it would also shield you from taxes on growth and on capital gains when you sell.