The response of the airplane depends on the airplane and the modes of autopilot and autothrottle engaged when the updraft is encountered.
In normal high-altitude cruise, VANV will effectively be in an altitude-seeking mode, and the MCP cruise altitude will be the target. The FMS or MCP Mach will also be the target of the autopilot and autothrottles. I don't think it matters whether it's Boeing or Airbus at this point; manual flight is a different story, though.
So, in a severe updraft, the pitch will initially go down and the throttles retarded in an attempt to maintain target altitude and Mach. If the throttles get to idle, pitch will continue to seek target altitude until limit Mach is reached. At that point a climb at limit Mach will commence.
If the updraft abruptly ends, the throttles will advance (likely to the CLB or CRZ limit) and pitch increased to attempt to maintain altitude. Altitude will be sacrificed to keep airspeed above the low-speed limit.
Again, with autopilot and autothrottles engaged, it doesn't matter if it's FBW or conventional, Airbus or Boeing. Response will be essentially the same.