Having a dd with a birthday just after xmas, I can agree that each occasion should be marked differently, with appropriate gifts.
Perhaps in future you might choose to celebrate her birthday on a different day, that helps us greatly as family tend to remember to think about separate gifts for her etc. Having more 3 dc in total, it wouldnt look good with the other dc getting lots of gifts on bday and xmas and dd getting a combi present!
I'll assume his son lives elsewhere, if so than Yabu he is entitled to spoil him a little and while I hope he would contribute to your daughters gifts, he is not exactly obligated to. You cannot expect him to treat both dc exactly the same. Even if it was his dd, I would think a non resident child deserved something extra, thats just me though.
I was/am a stepchild and when me and dsis (older half sis) were little, we knew my stepbrother got a lot more and some quite expensive gifts...it didnt bother us at all! Even then I understood that we had what he really wanted, which was his dad living with us and being part of our daily life etc.
Besides it was a given that each parent sorted their own childs gifts out, we didnt even really spend christmas day together, but would catch up boxing day. (DSbros mum wanted him every xmas day)
There was also the fact that Step bro and my Dsis had an extra xmas + presentz with each side of family, (well my sis only had her dad and his gf and her kids, no grandparents aunties uncles to spoil her so still pretty low key) while I never had another side of the family at all, my dad fucked off never to be heard from and his family never knew about me till i was older.
I still didnt complain or feel it was unfair and I think thats mostly to do with how my mum handled it herself, she was very matter if fact about it all and even at 3years old I understood our family situation.
It never ever occured to us kids that these arrangements were unfair, we were happy with whatever we got!
Humble lot we are!
If you think your dd doesnt have enough then crack on and get some more
Next year you must budget for her birthday and get it sorted a bit earlier.
If you two are not married or sharing finances and have no joint dc then as long as he's paying his way while under your roof, You have no right to complain about what he spends on his own child!