Our 9yo had a bday on debarkation day, so we celebrated the last full day, a sea day. No candles and no balloons onboard. We did a little decoration in room. You can buy decoration packages too, but they get put up at the beginning of the cruise - not a day you choose -ours was 11 night primarily for our 20 th anniversary, so we did not want bday stuff up the whole cruise. On the
Disney store website you can get bday invitations, so we got them printed with date, Main dining, location (North Sea), the ship (Disney Magic), her name and age. These invites cannot use WDW names however (see fine print), so it worked for the cruise. Kidsclub counselors were great- I mentioned her bdayto the counselor she bonded with and we received a hand made bdaycard from the counselor in our FE. We ordered cake for her bday and it was tasty and crew sang her happy bday at dinner last night. BBB is onboard most ship (all now?), so a great option as well. The spas have kids or tween packages I think, so another possibility perhaps. Birthday button too!
At the parks, there is a greater variety of places to go, eat at, etc. you can have candles and balloons. There are many more cake options -even some pretty nice character themed cakes that you can order ahead of time (on board there is a Mickey cake option, otherwise the cakes are custom based on cake/frosting/filling choices -no characters). Birthday button to wear. We've done an adult birthday at WDW, but lots of options. Princess meals - or other themed meals-plenty of options. When I took youngest to WDW for mom daughter trip when she was 5, we did 3princess meals, watched parades, rode only a few rides,watched more parades (her choice), BBB, and every night she crashed by 8 pm. And to facilitate traveling with a short legged, possibly very tired 5 yo, I did buy a small umbrella stroller at a resale store at home - great use of $8, as we would have never made it around world showcase without it.
Really, depends on what you see as fun for her and your group. Also, what kind of pace will work well. The ships are more relaxed in some ways,but you get to go to various new places. Parks are generally fast paced, but huge variety of experiences. Good luck with your decision!