I have the Givenchy Antigona and a Chanel Boy. I can't speak much for the Flap Bag since I don't own one but I do love both very much and get a lot of use out of them.
It's somewhat difficult to compare the two because what you really need to ask yourself is what exactly are you looking for. An everyday bag? Or a special going-out bag? (Although the Flap can be worn all the time).
If I HAD to chose, I would say the Antigona only because I've had mine for over a year now and love it more and more everyday. It's beyond the most practical bag I've ever owned! However, keep in mind that Chanel increases in prices frequently. Just think about what you REALLY want in a bag.