You framed the question as if you had a choice, but if the reimbursement was already paid, its a done deal.
The rules are this: if you are reimbursed for work expenses with tax-free money, you can't also take a tax deduction--you can't deduct the expenses from your income because the reimbursement was never in your income. If the reimbursement is less than your qualified tax deduction would be, you can deduct the difference. You can report your mileage using the standard mileage method which is I think 54 cents per mile for 2016. Then a few screens later turbotax will ask for any non-taxed reimbursement, enter the amount there. If there is a remaining deduction, it will be applied to form 2016 as a schedule A itemized deduction. But since this is subject to the 2% rule, your actual tax benefit will be limited based on your other tax facts.
In a nutshell, if you were reimbursed at 40 cents per mile, you can take an additional deduction for the remaining 14 cents, subject to the 2% rule. If you were already reimbursed at the full rate, there is nothing you can deduct. (And if you were reimbursed at more than 54 cents per mile, the excess is taxable income.)
If the reimbursement was added to your taxable income in box 1 of your W-2, you can take the full deduction against the taxable income.
In the future, if you have a choice between tax-free reimbursement and a tax deduction, the reimbursement will almost always be better because of the 2% rule.
https://ttlc.intuit.com/questions/2902781-what-is-the-2-rule
