Op firstly kudos to you for a reply that acknowledged the points that were made. No justifying, or arguing just a simple "thank you these are good points". I sometimes read responses and wonder how I would feel if it was my post, even if the points are valid and reasonable like they are in this thread.
I'm a second child and I carry elements of "my older sister had it better." Interestingly enough, as we've discussed as adults, my sister feels as though I had it better. Perception is everything!
Having said that, you acknowledge some favouritism in the past. I agree with other posters who suggest apologising unconditionally to your daughter. She's the oldest of your two children. There are different levels of experience with each child and things you learn. Parenting is not an exact science. From what I can understand, it's a learn as you go situation. I'm not suggesting you use the "learn as you go" argument for justifying the favouritism but just simply for your own peace of mind.
I go with apologise unconditionally - perhaps with some examples so you can show your daughter you know what she's talking about, not just saying you do, and then move on from there. Nothing that is done now will completely erase the past but you can move forward. Another suggestion if possible is to make special time with your daughter, doing things she likes to do now, one on one or you and your husband with your daughter. Not in a 'forced festive' way but in a way that shows genuine desire to want to.
Your daughter may never get past this (I don't know the level of favouritism we're talking!) but you can by first apologising, then rectifying so it doesn't happen again, and then you knowing you have done what you can.
Best of luck!