Originally Posted by
KL803
In short: there's no advantage. Personally, I always choose to book with the airline directly if ever possible. However, the itinerary in @Benjh's post wasn't bookable with AF hence the hint with "bookwithmatrix".
As mentioned, the « ITA Matrix trick » only really helps when trying to build complicated itineraries that don’t price out on AF/KL websites.
Sometimes inventory that shows on ITA Matrix isn’t available, but sometimes its even cheaper to book directly with the airline. My recommendation is to call up AF/KL and get them to build the itinerary (make sure to quote the right flight times and flight numbers, codeshares - even on AF and KL - DO matter).
Alternatively take a screenshot of the routing and send it through the AF facebook. They’ve been the best a making these routings plus they only charge the 6€ internet booking fee instead of the 40€(?) telephone booking fee.