There is no way I'd lug 15 big bins upstairs every year for Christmas decorating. Nope. Never. I have 4 bins of ornaments cuz we have a small 4' faux tree for our foyer and then DH talked me into a real tree this year, so I needed more ornaments--the whole back was bare! Then I have 1 small box of decor and a Rubbermaid bin of Christmas/winter dishware and kitchen towels. Oh, and holiday CDs, in case for some reason I lose all the MP3 versions on my EHDs.
Anyway, it sounds like you've already sorted most of it into one bin of the stuff you do use. That means you don't have to sort anything for yourself. You could just donate all those "extra" bins of decor. Yea! But it sounds like you're feeling nervous about that because of your kids, so I'm going to pretend to be your child for a second. What I write might seem harsh but that's cuz I am not a sentimental person. Also, I'm not actually your kid, so you might be like "Who is this Sara, pretending she knows things! She doesn't even like Christmas decor!" LOL (I just made a LO about the ONE Christmas decoration that I care about. I'd be happy putting up that and nothing else, even a tree. DH about had a heart attack when I first told him I didn't want a tree. He got his way about that.) Anyway, back to me pretending to be your kid and looking at all those bins: That one box of stuff that we all put out regularly, that I remember Christmastime, decorating and listening to music and drinking hot cocoa throughout the years with my family--that's the only box of stuff I care about. If 14 bins never saw the light of day, I'd probably not go through them, except to make sure there wasn't anything truly valuable (or misplaced) in them... but chances are, I won't even know if something is valuable cuz I'm not a Christmas decor appraiser. (Is that a job?!) But, before these items were in bins in your home, it sounds like YOU saw these decorations displayed in homes cuz it was your (grand)parents' decorations. And obviously that means these things have meaning to you or you wouldn't have 15 bins of it. And that's OK. So, what about taking a few items--no more than 4 per child, or some other low number--to set aside for your children. Write a note about why those items matter to you and why you think they'd matter to your child. Then, whenever you think the time has come to pass the items on, you can give each child the things that you think they'd like. My mom saved a few ornaments after my grandpa died (my grandma died when I was quite young). She saved the ornaments that mattered to them that she also thought I'd like. And, when I got engaged* she gave those to me, as well as a few ornaments that she'd been purchasing for me and using on our family tree since I was a baby. I'll be honest: some of those ornaments I didn't keep. They didn't mean anything to me cuz I wasn't old enough to remember her buying them or even putting them on the tree. So I kept what mattered to me and that I wouldn't mind hanging up on my own tree.

And that's the thing: you could keep every single item and your kids could throw it all away out of despair of going through all of it. Or you could give them items that hold special meaning to you--and hopefully to them--that they'll treasure. Then you can donate what's still in good condition and perhaps another family will cherish the decorations and create their own memories.
*I got engaged young for my generation. I'm going to give DD and DS their stuff when they move out after college. Cuz who knows when/if this-coming generation will move out, let alone get married?! LOL/COL.