Preface: I don't like either theme. I don't like the Pirates movies (although I kinda liked the Stern game) and I disliked/didn't know Maiden music so much that I inquired on Pinside about swapping the music out before I ever played the game.
Upon initial viewing, JJPOTC looks amazing. Played a couple games at expo and thought I wanted one. Went to play one locally a couple weeks ago and I feel 100% different. It just isn't fun. Best LOOKING game I've ever seen, hands down. The idea of lots of the toys is cool, but they just don't make for a game I want to play long-term. The ship is the coolest thing, but that is going to get SO old in a home environment.
Maiden on the other hand blew me away. I only played a Pro, but I have been back a couple times to play it more. SUPER fun risk/reward rules, and the whole package (layout, art, etc.) is great. I can even say I have no interest in swapping out music any more after playing it. The callouts are the main audio focus and the music is pretty secondary and works well in this implementation (again, coming from a total non-Maiden fan). I like some of the extra things included on the Premium/LE, and the Premium art is dope, so I'm actually going to buy one.
If you've already played them and both you and your daughter were leaning toward Maiden, this is a no-brainer. I know Pirates has supposedly deep rules, but if the game ain't fun...Maiden on the other hand is a great mix of "keep the ball alive" and learn the risk/reward strategy, as you already noted.