If you invest identically in either your Roth or 401(k), you have the exact same marginal tax rate whenever you pull out the money and any fees for the conversion are ignored, there is no advantage either way. If in addition to the previous conditions, the fees incurred are identical at the time of conversion, you're slightly better off to keep it in the 401(k).
This makes sense, because multiplication is transitive.
---------Case #1: Immediate Roth IRA Conversion------------
A. Do ROTH IRA Conversion Now, paying Tax rate (Tax)
(401k Start)*[1-(Tax)]=(ROTHI Balance)
B. Balance at Year (Yr) assuming an average Rate of Return of (ROR):
(Balance)Yr=(ROTHI Balance)*[1+(ROR)]^(Yr)
C. In terms of the Starting Balance, this can be restated as the following via substitution
(ROTHI Balance)Yr=(401k Start)*[1-(Tax)]*[1+(ROR)]^(Yr)
---------Case #2: Roth IRA Conversion at Year (Yr)------------
A. 401(k) Balance at Year (Yr), assuming a Rate of Return (ROR)
(401k)Yr=(401k Start)*[1+(ROR)]^(Yr)
B. Convert the lump sum at Year (Yr), paying Tax rate (Tax)
(ROTH LBalance) = (401k)Yr*[1-(Tax)]
C. In terms of the Starting Balance, this can be restated as the following via substitution
(ROTH LBalance) = (401k Start)*[1+(ROR)]^(Yr)*[1-(Tax)]
D. Rearrange terms
(ROTH LBalance) = (401k Start)*[1-(Tax)]*[1+(ROR)]^(Yr)
Note that Step C from Case 1 and Step D from Case 2 are identical. This is, (ROTHI Balance)Yr = (ROTH LBalance)
In the case of identical fees paid regardless of when the conversion is made, the only change is when the fee is paid. If the fee is paid today, that amount of money is lost earlier so therefore has less time to compound, all else being equal.
Of course the real world will never work out this way exactly, but it's good to keep in mind when thinking about Roth IRA conversions.