Well, I would do what Lazur suggested, but as usual, with my twist (I seem to do everything diff, but there are many ways to achieve the end result). For me, Inkscape never seems to put the nodes in integral coordinates, and if you add a stroke to the logo on either object, then part of the blue may still show through (I kinda see blue on Lazur's end result).
What I do is make a thin frame out of the blue part, and layer it on the top of the white zig zag. Same basic steps as above, just choose the blue background duplicate it, select both blue objects (I find it easier to turn one of the objects a diff color) and then move both to the side to work on. Turn both objects into paths. Use your ctrl + arrow to make the top object a little smaller, position it correctly, then do your path difference and you are left with a thin frame. Recolor the fill if need be and place it over both of your original objects and group them all. You won't see any blue peeking out anymore when lined up correctly. To each his own way!
dee
