The real challenge with spaces like yours is that neighbor noise comes through mainly via the walls, and here thin panels alone don't do much. Whoever told you to add mass behind them is right, but here's the part people often underestimate: panels absorb sound that bounces *inside* your room, they don't block it when it comes from outside. That's a huge difference. If you're hearing the bass from their stereo or heavy footsteps, what you need is to break the direct connection between the wall and the inside of your room, not just cover it with foam.
The system that actually works involves a layer of insulation (mineral wool, thick cork), followed by a heavy layer like drywall, and then an air gap between that and the original wall. Decorative acoustic panels, honestly, you add those afterward if you want to improve the internal acoustics - to reduce echoes and reverb in the room itself. But on their own on the wall, even if they look good, they don't stop noise from the building next door.
What worries me in your case, given that you're in a 70s building, is that before doing any work you should check the wall condition. If there's rising damp or condensation issues, adding insulation layers can make things worse by trapping moisture. It's worth doing a quick inspection first, maybe with a flashlight. And if you decide to do real acoustic insulation, do it on at least a whole wall: doing half a wall creates weird sound behavior that can end up being more annoying than before.