[berberous]

When people say it's the same, they are assuming you are investing the tax savings from using a traditional 401k. In other words, you could invest $10,000 in a Roth 401K, or $10,000 + ($10,000 * marginal tax rate) in a Traditional 401k. Then the numbers work.

[jaredsohn]

Another difference I just thought of (which may have been what I was originally thinking of but I said it wrong.)

I think an advantage of a Roth is that you don't have to pay tax on the money you earn via investing. For example, if your money in a Roth doubles then you only need to pay tax on the half of it that was there when you added money to the fund. Whereas for a traditional 401k you pay tax on money as it comes out which includes money earned via the investment.

[jaredsohn]

I made my prior (incorrect) analysis based on the math from this expression, despite saying the expression was wrong:

(i.e., tax_rate x (principal^gains) = (tax_rate x principal)^gains.

Gains should be multiplied rather than an exponential factor here. (I think this expression was created because gains are calculated as roughly (1+rate)^(number years) but at this higher level it should just be multiplied by the tax rate and the principal.