I have used a tax advantaged account (403b), which fortunately was low cost (Vanguard). However, there is a point to consider a taxable account, especially when there are high fees in the tax advantaged. In that case, you could contribute to get the employer's match, if any, and then do a Roth followed by taxable. IMO, if you plan to retire in your current tax bracket, a tax advantaged account does not benefit much, if any, as you pay the same tax either now or later:

tax rate*savings*(1 + annualized return)^number of years invested = tax rate* [savings*(1 + annualized return)^number of years invested}

If you plan to retire in a lower tax bracket, then the tax advantaged account transports your money to the new bracket, a very nice thing.

Your equations are off. Even if you retire in the same tax bracket there is still a benefit to a tax advantaged account vs long term buy and hold in a taxable account. The amount you end up with in the tax advantaged account is:

IRAValue = (1 - tax rate later) * savings * (1 + annualized return) ^ number of years invested

Meanwhile for the taxable account you end up with:

TaxableValue = (1 - tax rate now) * savings + (1 - cap gains tax rate later) * (1 - tax rate now) * savings * ((1 + annualized return) ^ number of years invested - 1)

(Where [(1 - tax rate now) * savings] is the amount you deposit into the account, and then [(1 - tax rate now) * savings * ((1 + annualized return) ^ number of years invested - 1)] are your gains, which then get reduced by a factor of (1 - cap gains tax rate) when you realize them.)

If your marginal tax rate now vs later is the same, the tax-deferred account is a huge win (by a margin of the long term capital gains rate). If you have dividends/capital gains over the course of your holding period, the advantage of the IRA is even bigger.

I find an easier way to think about it is to note that if tax rates now and in the future are the same, then a traditional IRA and a Roth IRA are exactly the same. I.e. deferring your taxes is exactly the same as not having to pay taxes on your gains in terms of how much money you end up with.

Edited: Fixed some typos.