A319 Captain reported that a known deficiency in older radar displays caused the flight crew to enter convective activity leading to a loss of aircraft control during approach. Crew recovered aircraft control and continued on the approach.

Narrative

Being vectored for approach to Runway XX from the west. Aircraft initially at 8;000 feet and 210kts. We were vectored north of convective activity and issued a descent. Our radar showed small convective activity and we asked and received clearance to deviate left 10 degrees which was enough as per our radar display.. Our radar however; without time to alter course; then showed the convective activity to be much larger. I made the required PAs to passengers and Flight Attendants who were already seated. I attempted to alter course but was unable in time to avoid the convective activity. The aircraft initially pitched up exceeding the autopilot capability and I had to take over as Pilot Flying. Our attitude deviation was well in excess of 300 high and our speed might have exceeded 250 knots but never exceed the aircraft limits. We rolled initially but not more than 30 degrees. While I had some control of the aircraft throughout and manually regained pitch after the autopilot disengaged ; I initially was unable to control the altitude without the probability of aircraft over speed as we were climbing and accelerating; thrust was idle; aircraft rapidly accelerating and climbing. There were two brief encounters; each probably less than a minute each. We exited the turbulence off heading and altitude. We reported the event to ATC who was very assistive in returning us to a good path to join the ILS. There were no injuries or aircraft load or speed exceedence.The radar units in many of our older Airbus aircraft have a known deficiency in both visibly and quality of return. This unit did not paint the convection until it was too late to alter course. Replace the older series radar.