Beautiful wands, @Liisa! You have quite a talent for carving and wand design 
Others have shared some wonderful knowledge about Birch and Willow- lots of great info here! Adding to that, I know @MeganB did some research on Sacred Irish Trees and wrote a post about the meanings and uses of Birch/ Beith as the wood is used in the Ogam alphabet and ancient Irish tradition. Just another resource for you to consider as you study the wood properties!
I think both trees have wonderful and unique benefits- I’m with Christina and Rown! If you’re up for it Lisa, why not decorate both lovely wands and use them for different purposes? At the very least, they would both make a beautiful addition to your altar space 
Happy wand making! 