If you expect to be in a lower tax bracket when you take the money out, then invest pre-tax money. If you expect it to be in a higher tax bracket, invest money after you pay taxes on it. Obviously this is a very simple way of looking at it. But I think it's a good way to get a general understanding of the different options. Post-tax investments can be good if you need to pull out a big lump of money while retired.
On top of that, since you are only feeling a 11k reduction in your paycheck per year, but investing 15k, you end up with that much higher growth overall starting with a higher base.
The only time expected retirement withdraw rate (treated as income at that time) matters is when choosing between Roth and traditional 401k / IRAs. In that case, with Roth you are contributing a lower amount initially (11k reduction in pay = 11k invested, instead of 15k invested), however the interest grows tax free. So if you are investing enough that the interest gives you a huge amount of money during retirement such that your annual retirement income (using 4% rule) gives you much higher pay, you would be better with Roth. But in no case are you better without any tax advantaged account.
i.e. I'd argue that most people will be paying lower taxes in retirement (even without moving to a low/no tax state) even if their post retirement income is greater than their pre retirement income and tax brackets haven't changed.
No, the grandparent is correct. The tax rates and compounding are both multiplicative, so associativity leads to the consultation that only the tax rate at saving-time and retirement-time matters
Pre-tax investment: Invest $100k and it becomes $200k. You pay $60k in taxes and end up with $140k. Post-tax investment: You pay $30k in taxes and invest $70k. That $70k becomes $140k.
Yes, technically with the latter you will have more money left to invest in a separate taxable account, but not being able to defer taxes will drag on the investment return.