So, the short answer is: usually lighter, but it depends on where the furniture is going. If you are talking about urban balconies, rooftop terraces, cafes, and small courtyards, urban outdoor furniture is often designed to be easier to move, store, and rearrange. That means you will see a lot of aluminum frames, powder-coated steel, HDPE, recycled plastic, synthetic rattan, and sling fabrics. These materials can give you the look of wood or wicker without the dead weight. A typical aluminum bistro set or modular sofa can often be lifted by one person, while a solid teak dining table might need two or three.
Traditional wooden sets are usually heavier because the material itself is dense. Teak, acacia, eucalyptus, oak, and mahogany are sturdy and weather-resistant, but they are not light. A wooden table and chairs can also be bulky, which makes them harder to move around a small city space. That weight is a benefit in windy rooftop conditions, though, because it helps keep things from sliding or blowing over.
But there is a big exception: public urban outdoor furniture. Benches, tables, and seating in parks, plazas, and transit areas are often extremely heavy. They may be made from concrete, cast iron, thick steel, or stone, and sometimes they are bolted down. The goal is not portability; it is durability, vandalism resistance, and staying put.
So, for residential urban spaces, urban outdoor furniture is typically lighter than traditional wooden sets. For public, heavy-duty urban environments, it can be much heavier. It really comes down to whether the design prioritizes flexibility or permanence.