I think they are very similar when you say them out loud, but if you mainly use the nicknames it might be ok? It's the "Mill" sound that might be an issue but as a pp said it may come down to accents. They are both beautiful names. I know of a local family who have an Emily and a Millie which makes me every time I hear!
I see where you're coming from, since they have the same rhythm and a lot of the same sounds in the same places, but I think it's fine. They're very distinct names to me despite sounding similar if that makes sense - not like Maisy and Daisy or Juliana and Liliana or something which I think of as being under the same umbrella of names.