I think all Birdy bikes have hands off shimmy due to the folding mechanism, but thankfully no hands on shimmy.
The difference between even the Marathon Racers and the Stelvios is night and day. I recently had to ride with a Racer on the back and was dropped by folks that don't usually drop me! The Birdy Maxis is even worse.
Of course, nearly all of the performance difference between one bike and the next is due to the wheels and tires, at least on flat surfaces. The 24 spoke wheel with a relatively light rim is great. The Maxis is not so great, but gives a more confident ride.
That is where I think the only real trade off comes in with a small wheeled bike. If you ride thin tires on small wheels, there is a danger that the wheel can sink into a pothole or grate.