Assuming my math is correct and that I'm not missing something about Roth investments, it appears to me that either option will work out exactly the same if you will be in the same tax bracket in retirement.
This is true only if your average tax rate in retirement is the same as your current marginal rate. I'm surprised none of the answers mention this since it is the crux of your question!
If you can deduct an IRA against your income taxes, it is almost always better option than the Roth equivalent. Marginal rates should not be compared to average rates or you will form all sorts of inaccurate conclusions.
"If you are in a lower tax rate in retirement traditional is better" really means, "if your average tax rate in retirement is lower than your current marginal rate, traditional is better" - which for the overwhelming majority of Americans is the case.
Consider the following. Let's say your intend to contribute $1000 in one year (making $2k) and withdraw it the next that is your only income in that year. Your tax brackets look like:
- First $500 income, 0%
- Everything above $500, 15%
This is quite simplified but for this purpose will illustrate precisely why comparisons like you are making are very misleading.
In this case you can put $1000 in and pay no income tax at all (because you deduct it). You then withdraw $1000 the next year. The first $500 you withdraw you pay no taxes on and the next $500 has a tax rate of 15%, for a total tax of of $75.
However - this is a tax against your entire withdrawal of $1000, so your average tax rate (this is important! average is different than marginal) is only 7.5% and you are left with $925.
In this case you can only contribute $850 to the IRA because you are taxed against the money at your marginal rate (15%).
When you withdraw it, you don't pay any taxes and are left with the entire $850 $850. This is less than the above, because you are taxed the whole amount at your previous marginal rate.
If however your tax rate in retirement was 30% for everything above $500, only then are the two scenarios equal. Your marginal tax rate in retirement has to be very high relative to your current tax rate for the Roth to ever catch up and be better.
If you are able to deduct an IRA contribution, it will almost always be the best option. The average federal income tax rate on middle class families has not changed dramatically enough over the past 50 years to be above normal marginal tax rates - even at the 15% federal tax bracket, your marginal rate is still higher than the highest average tax rate for the past 50 years by at least 3% and normally significantly so.
The reason I make this point about middle class marginal rates is that the majority of "taxes might be higher in retirement!" is very unlikely to be the case in a meaningful way given the past 50 years. However if you are in the top tax rate you are paying historic low tax rates (by a factor of nearly 3), but also observe you can't do either IRA since you must make $400k/year. The difference for middle class is no where near as noticeable.
Keep in mind if you can't deduct, there is no reason to not contribute to the Roth.
There are other factors contributing to the traditional/Roth decision. This answer only addresses the specifics in your question.