Which trip would be better?

I have never been to Andorra, but have been to Barcelona (three times) and the Basque Country.

Loved both Barcelona and the Basque country. If you do the Basque Country, consider doing a couple of days in the Bordeaux region of France, just across the border.

Depends on the length of the trip, time of year, and how often you want to change hotels. Andorra la Vella can easily be skipped. Other parts of Andorra are supposedly very pretty, but you may need a vehicle to get around.

For the Basque Country a rental vehicle might make traveling between places more convenient depending on where you want to go.

No car needed in either Barcelona or Bilbao. There is no better, just which you prefer depending on what what you want to see and do.

Have not been to Andorra. But we did a wonderful road trip that combined the Basque country and Barcelona: We flew into Barcelona and drove directly to Zaragoza; then to Vitoria-Gastiez via Laguardia; to Bilbao; to San Sebastian; then to Hondaribbia with a daytrip to Sare, Ainhoa and Espellette, FR; to Bayonne via St, Jean de Luz; to Carcassonne; then, via Figueres, back Barcelona where we dropped the car before exploring. Our trip was about 14-15 days on the ground which worked well for us but you could certainly spend, and enjoy, much more time along the way.

Happy planning!

Just spent an entire month in Basque Country and Catalonia.

If all you have is two weeks, either one fits the bill.