Well..I think everyone's a little bit right here, depending on what question is being answered.

Suppose:
- George and Martha each have $10,000 in a traditional IRA, and another post-tax $10,000 in cash, and
- on day one, they both a) convert the traditional IRA to a Roth; b) pay the taxes due; and c) put the cash account to work in a taxable brokerage account, and
- they choose identical investments which are destined to double in ten years i.e. just under 7.2%/yr
- and their marginal tax rate is identical now at 24%, and will be the same in ten years

The only difference is that George pays the $2400 in Roth conversion taxes from the IRA, and Martha takes it from the cash destined for the brokerage account

In ten years: yes, their monthly statements read the same: $10K plus $7600 have each doubled
- George has $15,200 in the Roth and $20,000 in his brokerage: total $35,200
- Martha has $20K in her Roth and $15,200 in her brokerage: total $35,200.

So, if the question is, who has the bigger statement balance in ten years? the answer is, multiplication is commutative etc

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But if the question is, if they each cash out of both accounts at the ten year mark, who can buy the bigger boat?, then:
- George gets $15,200 from his Roth and ($20,000 less 24% =) $15,200 after tax from his brokerage, or $30,400
- Martha gets $20,000 from her Roth and ($15,200 less 24% =) $11,552 after tax from her brokerage, or $31,552

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But if the question is, how does their son John fare estate-wise when they both die while looking at boat catalogs at the 9.99 year mark?, the answer is:
- it depends - to a large degree, whether John inherited his money management skills from his mom or his stepdad, but also estate size, other assets, probate regardless? etc.
- but often, better with Martha's
- and George and Martha never got their boats, so there's that

-- sutton