Dries hotter and faster (clothes come out warm and toasty, although apparently that's actually not good for them) and dries larger loads.

Downsides are that it requires more space and is less energy efficient because instead of repeatedly recycling an internal supply of hot air, each load is washed with air pulled from the space around the dryer which is probably air conditioned and therefore needs more power to get hot enough.

In the US at least, vented ones are also significantly cheaper to acquire, but that might be an economy of scale thing.