This has been answered above a lot of times by different people. But I will share my experience and decision of moving away from Honda City. I've had 3 Honda City's include 1.5 and 1.3 (all MT) and I have also driven a friend's 1.5 AT extensively.
Before I test drove Yaris (it was 1.3 GLi CVT) I had the same understanding that it would be highly unstable above 120/140 because of the raised height and softer suspension. When I test drove the car (it was a long drive of about 1200km) on M2, Lahore/Multan GT Road, within City (Lahore and Islamabad).
The car is not at all unstable - I can't comment on the stock tyres because the car I drove was with Continental Tyres (185/65) and after market alloys. But it was extremely smooth. On M2, the car was very stable, even at the speed of 120/130 the cabin noise insulation is just stunning. The low end torque feels really good in city driving conditions and even on GT Road. The suspension handles our roads very well. Braking is good, I had to apply emergency brakes a couple of times due to truck drivers changing lanes abruptly. The manual shifting option is a really good feature as well. 1.3 isn't underpowered either. Fuel average is pretty amazing as well especially on long routes. Overall it was a good experience. Much comfortable ride compared to City.
However, like every other car it has its pros and cons. I love Manual transmissions, so I didn't like the rubber band effect of CVT. Position of Arm Rest isn't good. Softer Suspension has its pros and cons but atleast I didn't had to worry about speedbreakers hitting the car. Handles bumps, potholes pretty good in comparison. Seats are very comfortable compared to City but I do feel like seat hight adjustment should have been there, would make the driving experience a lot better. Reving the engine on higher rpms doesn't feel as good as it did on City.
Bottom line, if you want a car to take you from point A to point B comfortably and peacefully Yaris is the way to go. If you like to rev the car and like to drive fast around the corners City is the way to go.
And people commenting about it's build quality - it is better than the current Honda City. Let's see what Honda comes up with in the 6th Gen.
Edit: based on this experience I decided to go with Yaris. Expecting it to delivered next month. I went with 1.5 CVT because even though I didn't like the rubber band effect much but I needed an auto transmission