Generally speaking, claiming a foreign tax credit is better than claiming a foreign tax deduction. The simple reason here is basic math. A tax credit of any kind represents a dollar-for-dollar reduction in your income tax liability, whereas a tax deduction just reduces the dollar amount of your income that is subject to being taxed. Thus, a single $1 tax credit is worth exactly $1 toward your overall tax liability, while a $1 tax deduction is only worth ($1 x your marginal income tax rate) toward your tax liability.
So, where a taxpayer has a choice to make, it's usually better to claim a credit than a deduction, if they can do so.
We also have some TurboTax articles on the foreign tax credit that you may find both helpful and interesting. Here are a pair of courtesy links to those:
Thank you for asking this important question.
Why does TT ask the user to make the decision instead of figuring out which reduces the tax the most?
Given that the foreign source income entry is non-trivial, maybe it could give the choice as "just take the deduction" or "allow me to enter information for TT to decide."