The big advantage of putting your additional contributions into the 401(k) is that it reduces your taxable income. The big disadvantage is that the money is locked away for decades; that cash is no longer available to make big purchases like a car, honeymoon trip, etc. There are some exceptions, but be careful that you don’t get hit with penalties.
Personally, if I were in your situation, I would open a no-fee brokerage account and put you additional retirement money into an index fund that tracks the S&P 500 or NASDAQ. If you need the money before you turn 66 then it will be readily available.