First a preface that those are all reliable kites from established brands. They're all good in that regard.
They're the same class of kites. All of the kites you mentioned are parafoil speed kites. "Para" with its roots the same as parachute, the kites have no spars. "Foil" referring to the airfoil shape, similar to an airplane wing with internal cells.
There are several sub-classes of parafoil kites. Those are speed kites, the bridle lines on the kite put the kite at an angle to make the kites move quickly, even in relatively light wind. You are right that these kites feel twitchy, that's because they are speed kites. Among the other sub-classes of parafoils, one popular style is traction kite or power kites which can have enough pull for buggies or skiing, and another popular style is lift kites or show kites that are large and stable rather than being designed for agility.
The twitchy feeling is part of the style. All the parafoil speed kites move quickly and are sensitive to input. They CAN fly in a straight line, but it requires experience and skill. They are not designed to move slowly like kites designed for slackline tricks, nor move like quad line kites. Fast and nimble are intentional.
Some difference, but they're similar because they're all the same class of kites.
The bigger kites have a bigger sail area and generate more pull. The 1.3 is 130 cm across, relatively small. It has bigger brothers at 180 cm and 220 cm that can generate more pull. The Synapse family has similar sizes at 140 cm, 170 cm, and 200 cm.
All of those sizes are still in the speed kite category. Parafoils are not usually considered power kites or traction kites until they reach about 3 meters across. (Different people use the names differently, commonly power kites are 2 line, traction kites are often four lines, but that isn't universal terminology.)
Turning speed is going to be a matter of several factors. The wind speed, the kite's bridle configuration, and the pilot's body movements will all make a difference. Bigger kites tend to have more drag (slow down) due to their size, but with some experience a pilot could make a small kite turn slowly and make a large kite turn rapidly. Even so, they're all parafoil speed kites so they're going to turn fast and fly fast.
The kite is marketed as a beginner kite. Parafoils are very resilliant kites because they don't have spars (no parts to break) and this one is smaller making it more gentle than it's bigger brothers. Combined this kite is easier for beginners, but that doesn't mean experienced people can't or won't fly it.
If you like the parafoil style consider keeping the smaller kite in your bag and picking up a larger model. When winds are strong a large kite can be damaged or be overpowered, the smaller model with less surface area can let you have a similar flying experience.
Whatever you decide to do with it personal preference is important, fly what you enjoy flying.
If you live somewhere near others who fly, such as on a beach or near a kite store, consider asking about flying a variety of kites. Many people have a collection of different kites and will help you experiment a bit to find kites you enjoy. Flying other people's kites is the cheapest way to go when starting out. You'll be addicted in no time. ;-)