Think about the sort of riding you do. Is it all in town through heavy traffic? Or does it include some open road with hills, bends and overtaking opportunities? If the world was a logical place, everyone would choose an automatic for the first scenario, and a geared motorcycle for the second.
But the world isn't any such thing, and a lot of personal preference comes into the decision to take an automatic scooter or a geared motorcycle. Not only that, but some motorcycles are semi-automatics, and are neither one nor the other.
The pros and cons of the automatic transmission are as follows. First and most obvious is convenience. There's no clutch to worry about, no gear to select, and consequently less to think about all-round. Maintenance is simpler, as the drive-belt doesn't need lubrication and adjusting. On the other hand, an automatic is less efficient than gears. Drive-belts also work hard and don't last quite as well as a chain, though this varies quite a bit from scooter to scooter. And the flipside of an automatic is less control, so you can't change down to gain engine braking, say down a steep hill or corning up to a sharp bend.
As for a manual transmission, this is part of the fun of riding. Feeling the gears snick home neatly, changing down to the right ratio for a bend, then back up through the gears as you accelerate away. A chain is more efficient than an automatic, and drive-belt found on most automatics, and as you've got the choice of hanging on to a higher ratio, geared motorcycles are potentially more economical.
The downsides are that a clutch and gears can be tedious in endless stop-start traffic, they're also a headache for some novice riders, and that vaunted efficiency drops off if the chain isn't kept lubricated and nicely tensioned.
So, geared or automatic? It all comes down to the sort of riding you do, your affinity for maintenance... and personal preference.