Flat cords are for lamps. Round cords are for power tools.
It depends on what you’re plugging in. That’s really the whole answer.
Flat extension cords are designed for low-wattage stuff — lamps, phone chargers, a small fan. They’re thin so you can run them under rugs or along baseboards without a big bump. But they can’t handle much current. Plug a space heater or a vacuum into one and you risk overheating or a fire.
Round cords are thicker, more durable, and built for higher amperage. Think power tools, space heaters, refrigerators, anything that draws real power. They also tend to have better insulation and grounding. The tradeoff is they’re bulky and you shouldn’t run them under rugs (that traps heat).
So: flat for light duty under the coffee table, round for anything that gets hot or draws more than a few hundred watts. If you’re unsure, go round. It’s the safer bet.