Wow what a tough decision, they're both gorgeous.
I used to have the fuchsia/mono and I really enjoyed the lining color, it's great to match with other fuchsia items if you're considering getting a wallet or key holder with fuchsia interior. Mine was damaged and I replaced it right away with another mono NF in cerise color. I think the mono NF is a classic and I love having it in my collection.
I also have the azur NF, and I love this bag too! mine is the older model with the white interior, I use a bag liner inside to keep the interior clean. I've had this bag for like 3 or 4 years and I don't have any color transfer, but I only carry it on sunny days with light outfits, to me this is more of a seasonal item.
Depending on what other bags you have, I'd say go for the mono/fuchsia, you would use it a lot, or for a fresh pop of color go with the azur, gld!