Bryony because that's the usual and correct spelling and choosing another variant will lead to years of you and her having to correct people. Trust me where i work I register people (library) and unusual spellings cause so many issues. It also looks better, plus Briony is like you have named the child after a Brian and added on a y to make it feminine.
wildpoppy - everytime i give somebody my name i have to spell it out, sometimes twice, get some funny looks and the 'thats unusual' comments. it doesnt seem much, but when you have to do this through out your whole life with nearly everyone you meet, it becomes pretty annoying very quickly!
plus when i was a child all i ever wanted was to walk in a shop and buy a teddy, mug, door plaque etc with my name on it like and i never could. plus the obligatory 'ha brian!' comments in the playground. in a class full of hannahs, sarahs, rebeccas erc i stood out like a sore thumb when i just wanted to have a normal name to be like everyone else.
although this probably wouldnt affect your daughter because there are so many children with unusal names it becomes less of an issue
its just personal taste at the end of the day, i find it dreadful but then does anybody really love their own name?