Having not flown a wide body forgive my potentially dumb question. Is it really that big a difference between an A320 to the A330/340 and Boeing 738 to a 777 or 787?
Having flown A320/A330/A340 the answer is no.
Long haul flying requires a lot more focus on flight planning and entry requirements as you cross various countries.
Entry requirements at various Airlines may be a Local CAA requirement that the Airline has no control over.