Munich or Frankfurt airport to Rothenburg?

If you're not going to have a car for anything else, then you don't need it for Rothenburg-ob-der-Tauber. The train trip is easy enough, but includes two connections from Frankfurt airport and more from Munich airport. Looking Up Train Schedules and Routes Online gives you the DB train schedule link and tips for using it.

Neither FRA or MUC is handy for Rothenburg. What are your OTHER destinations in Germany besides Rothenburg? Rothenburg is a small place that you can see in a day or less. It would make sense to fit it into your other plans - if it fits, that is. There are numerous old-world towns scattered about Germany with half-timbered buildings, cobblestones, old town walls and towers. And quite a few of those aren't nearly so overpopulated with international tourists.

It's going to take about 4 hours from either airport to Rothenburg. That's by regional train.

Using a fast ICE might shorten the trip a little, but will cost around a 100€ for two people with a full fare ticket. You don't want to use a train specific, non-refundable Savings Fare ticket on your day of arrival, because a late flight would ruin everything.

From Munich airport, you can use a Bayern-Ticket, 31,-€ for two people, all the way to Rothenburg.

From Frankfurt airport, you can use the Bayern-Ticket from Kahl am Main, the first stop in Bavaria on the RE from Frankfurt Hbf to Würzburg, but you will need an additional local, RMV ticket to Kahl, at 8,35€/person.

Where are you flying from? Lots of direct flight options to FRA from North America make it easier and probably less expensive airfare.

I am trying to determine whether it would be better to fly into Frankfurt or Munich. Assuming that the best way to get to Rothenburg from either would be via train.

The trip from Frankfurt is much faster (fastest connection is 2:30). Take the ICE to Würzburg, then the regional train bound to Treuchlingen and transfer at Steinach bei Rothenburg to the Rothenburg shuttle.

Since you seem to be flying out of NYC, there should be plenty of direct flights to both. Is one significantly cheaper than the other, flying at a good time for you from a convenient airport?

As has been pointed out, from Frankfurt airport, it is about 2 3/4 hours using ICE connections and cost about 102 EUR for 2, or you could travel in 3 3/4 hours with regional trains costing 52 EUR (Q.d.L. ticket) for 2.

From Munich airport, it is about the same for regional trains or with ICE trains, about 4 hours, but costing 31 EUR for 2 with a Bayern ticket

So add it up both ways with airfare to each airport, decide if you want to spend extra money to arrive an hour sooner, and you will have your answer.