I'll add a couple of things based on 1)riding my mom's 90cc 70's Vespa and 2)braking technique I learned in downhill mountain biking course.
1) That Vespa has horrible front end dive under braking. It shifted the weight, actually, kicked the weight forward. Almost felt like it was trying to launch the rear wheel off the ground. Your new scooter may dive more than your old. If it's bad, you might want to get a stiffer front spring. Additionally, a firmer damper can help.
2) Our mountain bike teacher showed us that he could go from 20 mph to a dead stop in just one bike length. I went from about 10 bike lengths to about 2. Granted, there's a lot less weight on a bicycle, but the technique he taught was amazing. Basically you push your heels down below the pedal as you are coming to a stop while shifting your ass to the back of the bike. It drives both tires into the ground. It's hard to do this on a scooter, but it is an active braking technique that will give your rear wheel more grip.
And like a lot of other people said, slow before the corner, slightly accelerate out of it.
Be safe everyone!