That's a great and very practical question for anyone managing public spaces. From my experience, there's a clear winner when it comes to pure vandal-resistance: metal bins, specifically heavy-duty steel models.
Plastic bins, typically made from polyethylene, have their advantages. They're lightweight, corrosion-resistant, and often more affordable upfront. However, they are vulnerable to certain types of vandalism. They can be easily scratched or carved with graffiti, which is difficult to remove. More importantly, they are susceptible to melting or warping if someone sets fire to the contents inside, and they can be cracked or shattered with sufficient force.
Metal bins, especially those made from robust galvanized or powder-coated steel, are inherently tougher. They are much more resistant to impacts, kicks, and attempts to dent them. While they can still be scratched or spray-painted, graffiti is generally easier to remove from a smooth, coated metal surface than from porous plastic. Their most significant advantage is high heat resistance, making them far less likely to be damaged by fire.
That said, "vandal-resistant" doesn't mean "vandal-proof." Determined individuals can damage anything. The choice often comes down to a trade-off. Metal bins are heavier (harder to tip over but more difficult to install), can be prone to rust if the coating is compromised, and are usually more expensive. Plastic bins are easier to replace and won't rust, but you might be replacing them more often in high-vandalism areas.
For a low-traffic, calm park, plastic might suffice. But for city centers, transport hubs, or areas with a history of misuse, the long-term durability and strength of metal bins typically make them the more vandal-resistant and cost-effective choice over time. The best modern designs often combine materials, using a metal outer shell for strength and a removable plastic inner liner for easy cleaning, offering a practical compromise.