Aircraft wasn't parked at the gate, not out of the "envelope" required by the moving airliner. Pilots of the moving aircraft should have noticed that other plane was a bit too close, but i'm sure that's easier said than done perhaps.
While you develop a feel for where your wings are, they are not visible from the cockpit on many airliners. On the 747-400, for example, you could see the wingtips, but on the 757 and 767, you cannot.
We have many SOPs to address safe ground operations; FO & Captain both check their sides before moving the airplane and verbally confirm "clear", FO & Captain both check their sides when turning the airplane and report "clear", FO reports "heads down" to the Captain if the airplane is moving and the FO needs to look inside. All obstacles must be cleared laterally, they cannot be cleared vertically (have to go around things, can't go over).
In this ramp area, ATC doesn't have control, so, technically, it's "taxi at your own risk"...but that onus is not well communicated to flight crews. You'll notice that this strike was on the FO side...and FOs have a lot to do while taxiing (checklists, confirming FMC entries, making new FMC entries, starting engines, etc.). This is why the "heads down" communication is so important...
I've got folding money that the FO was heads down, and the ramp cleared the airplane to taxi...but the crew didn't understand that ramp wasn't ATC and that the onus for safe operation (wingtip clearance, in this case) was on them. In the JFK case, the A-380 was cleared to taxi by ground, but the RJ wasn't visible to ground and they were waiting to park.
The important point is this: while ATC may clear you for something, it's your duty to refuse a clearance if you believe it to be unsafe. Too many pilots put blind faith in ATC. You must follow ATC clearance. This is drummed into you from the beginning, and controllers do not take kindly to being questioned on their instructions, but there are times when a simple query from the flight crew points out an error, and a simple refusal to accept a clearance ("Unable") will resolve an unsafe situation.
The A330 wingtip looked relatively unscathed, but that A-320 tail was severely damaged. Depending on the degree of damage, and the age of the airplane, i might well be a write-off. The tail itself is mostly composite, and a bolt-on affair. That's the easy part. The attachment points to the fuselage are part of the fuselage structure. I don't know how they would be tested, but they need to be tested as part of the repair.