I love both of them. I love my LV Damier because I can dress it up or down (papillon). I don't use my Fendi much either.
Since you want to be generous to your sis... I have questions do you have a problem with the handles on the bucket falling off your shoulder and do you use it at all? If you love the pattern but are tired of it only then would I keep it because you probably would use it again.
I love the Fendi flap, its a great spring bag and doesn't scream pink... but if you never use it and don't like pink at all then I would pass that. LV will always be around and if you did keep it I think you could sell it on Ebay faster than you could the Fendi.
Just read up...if she uses Dior she may love monogram and love the Fendi. If you want color in your wardrobe and can afford a bag with color for approx 110. look at the talbot bag Issmom was talking about its adorable.