Watts is a measure of power like an engine's horsepower
Amps is an instantaneous measurement of current, so it's like fuel flow rate.
Amp-hours (at a given voltage, 36V for instance) is an overall energy, like fuel in the tank.
To get Watts, you multiply the Voltage and the Amps.
A 36V motor at 12.5A is 450 Watts.
If you have (3) 12v batteries, with 10Ah each, you could nominally pull 450W from them for 48 minutes before fully draining them. The real world reduces this significantly. First, in Sealed Lead Acid batteries (Absorbed Glass Mat) the Ah rating of a battery is measured for 20 hours of discharge, and to full discharge. If you run a battery to 100% discharge, it is pretty much a 1-use item, the lead plates sulfate and cannot be recharged. Also, at faster current draws you get less total capacity.
Generally for SLA/AGM batteries you don't want to run to more than 50% discharge. Hopefully you are also not putting the full rated power through the motor on a constant basis.
Another factor you may wish to include in your scooter/cycle decision is how they are treated under the laws in your area. In the US, the federal law exempting electric bicycles from regulation as a motor vehicle goes up to 750W (continuous) rated motors and 20mph. The federal exemption also requires the bicycle is still a functional bicycle. I have not been able to find very good information on the regulation and exemption of electric scooters. Supposedly in California, they have some sort of exemption similar to electric bicycles, but part of the exemption requires you only run scooters on roads with a speed limit of 25mph or less, or in marked bicycle lanes and paths. Electric bicycles can run on almost any road (unless specifically posted as prohibited, ie. freeways) as they have much broader protection under the law.
Service life and range of batteries seems to me to be the biggest limit right now on e-bikes and e-scooters. When you factor in the cost of replacement batteries, e-bike commuting appears to cost around ~$0.13/mile.
For instance, Tim Lockard writes in his Lockardtechnologies forum about his Wilderness Electric conversion kit experience. It is a similar system, with a 36V ~500W brushless motor, and he paired it with (3) 12V, 12Ah battery kit (very typical for this type of kit). The batteries probably run about $80-$100 delivered (12V 12Ah seems to be at the price "sweet spot" right now for batteries. You pay more per Ah for smaller and larger batteries), and he was able to get 850 miles out of them before replacing them. According to his forum posts, he is an avid e-commuter, and runs somewhere around 8-10 miles each way. Obviously it is hard to estimate how much pedalling he does. For his experiences, see:
http://www.lockardtechnologies.com/cgi-bin/yabb/YaBB.cgi?board=ebike1. He had even worse results from his second set, they only survived 400 miles before he had them replaced under warranty. Their replacements didn't fare much better.
It seems like his batteries only survived ~120 charge/discharge cycles. I am told this is to be expected for deep discharges and high rates of discharge.
I haven't been able to find any other "real world" experiences with as much detail or longevity as Tim's. If you find other experiences posted on the web, I'd love to see them. Right now this is the biggest sticking point on whether or not I am going to get a conversion kit and start a bike commute in to work.
-Mike