It'll have a few advantages:
1) It'll be cheaper in the long run... I'm already on my third battery in just 3 years. The first one got weak and started burping battery acid all over. The second one had a cell die. The third one is currently in service. The ultracapacitors are rated by the manufacturer to last 10 years. They'll probably last longer, as there'll be very little opportunity for them to experience too high a temperature or too high a voltage.
2) No battery acid, so no battery acid burping all over the place. Had this happen twice with the original battery.
3) They can output huge amounts of current without voltage drop. Whereas a battery's high internal resistance drops the output voltage when it's loaded, the caps won't do that. So the starter will spin a bit faster, and while it's spinning, voltage to the spark will be higher, making for an easier start.
4) They charge more quickly, and don't boil or burp hydrogen or acid like batteries. Batteries start gassing even before they're fully charged. And God forbid a cell is weak, it'll start gassing like mad and burping acid, even if it's a sealed or AGM battery.
5) The AGM batteries (which I currently have) have a problem where due to the flow of electrons, it tends to wick the battery acid toward the positive terminal of each cell, leaving the negative end of the cell starved. This causes a drop in battery capacity.
6) About 5 pounds weight savings. And that's weight that's high-up on our bikes, so it'll lower the center of gravity.
7) Can be run all the way down to 0 volts without damage. Whereas a battery can be damaged if you get it down below 9 volts or so.
8) While I don't experience freezing weather here except for maybe one or two days every few years, conventional batteries experience reduced capacity in cold weather, whereas ultracapacitors don't. Not a big consideration for me, but for others considering this, it might be.
There's a guy on YouTube who's running this exact setup in his car, and it appears to run alright, so in a scooter, it should do just fine. He started with the larger ultracapacitors, and decided to try the small D-Cell types to see if they worked, as well. They did.
The only difference with my setup is that I'll be putting it inside an empty motorcycle battery casing, so it looks just like a regular motorcycle battery.