One difference is in the ability to split the pre-tax and after-tax portions of the Traditional account. (Note that earnings in a Traditional IRA or Traditional 401(k) are always pre-tax, even if it was earned from after-tax money, so if you left the money for some amount of time after an after-tax contribution, chances are it's a mix of pre-tax and after-tax money.)
When you take money out of a Traditional IRA, including for conversion to a Roth IRA, you are generally subject to the "pro-rata rule", which means that your withdrawal will consist of pre-tax and after-tax amounts in the same proportion as in your whole Traditional IRA. This means that a conversion of a Traditional IRA with any mix of pre-tax and after-tax amounts, will always be taxed on a portion of the withdrawal (the pre-tax portion), and it will leave some after-tax amounts in the Traditional IRA unless you take everything out. The only way to separate the pre-tax and after-tax amounts is to roll over to a Traditional 401(k) (if you have a 401(k) plan that allows this); rules say that only pre-tax amounts can be rolled over into a 401(k), so only pre-tax amounts are rolled over, and if you roll over all the pre-tax amounts, only after-tax amounts will remain.
On the other hand, when you rollover your entire Traditional 401(k) to IRAs, you can choose to have the pre-tax portion rolled over to a Traditional IRA and the after-tax portion rolled over to a Roth IRA, separating them, due to IRS Notice 2014-54.