Does it matter who the primary card holder is if both people have high credit scores?

It doesn't matter who gets the card. However, the credit limit is oftentimes based on your income. You alone would likely qualify for a higher limit than your wife alone would. Some credit cards allow you to include your household income in the profile, and in that case, your wife would have the option of including your income to get a higher credit limit. In that case it really doesn't matter who gets it.

If you're curious about the affect on your credit scores, the person who has the card in their name will see a slight temporary dip (2-6 months) due to the credit inquiry and reduction in the average age of accounts (AAoA), but once the card reports within 60 days, usually you'll see a credit increase due to the lower overall utilization percentage (assuming your total CC monthly spend doesn't also increase along with it). In general though, you're both doing fine with credit and I wouldn't really think twice about the minor changes in your score. Get the card that makes the most sense for your family.

As ceejayoz astutely pointed out in a comment: my disclaimer in the previous paragraph "assuming your total CC monthly spend doesn't also increase along with it" would not be true if your wife gets the card. She would be going from 0% utilization to something greater than that, and her AAoA would certainly drop. It's possible in her case that her credit score would drop noticeably more than yours would because of adding the new card, at least in the short term. I personally wouldn't let that discourage you though. In the long run taking that minor dip now is actually better for future credit.

Side notes that I always recommend for anyone who has credit cards:

1. Set up alerts such that you get notified for every purchase made on all of your cards (e.g. text/email/mobile app/etc). This way you won't forget about moving any automatic payments over, some of which may only charge annually. Another advantage of this is if any of your card numbers is ever compromised, you'll find out instantly.
2. Set up all of your CCs to auto pay (at least) the minimum each month. Still always pay in full, but if you ever forgot to make a payment, you might have to pay interest for a month, but at least you won't have a late payment which could adversely affect your credit for many years.