White on white isn't easy (my hi-key white poppy in my main album). Played around with the photo in LR after seeing a suggestion from Hazel (@quietpurplehaze) that white on white is better/easier in B&W. Still not particularly happy with this, may try shooting in B&W and get the hi-key sorted with the camera)
White on white does need some shadow, to give depth. You could perhaps add shadow to the poppy without greying the white, which would make it look less blown out and alter the contrast so the leaf and bud have definition and less shadow?
I actually prefer the first you posted though.