Let's begin with some essential principles of racquet physics:
The long axis of a racquet is the imaginary line from the end of the handle to the tip of the frame. If you put the tip of your racquet on the ground and give the racquet a spin, the long axis is the line around which the racquet rotates.
When the ball hits your strings above or below the long axis, your racquet's response depends mostly on how much weight is in the racquet head, how far from the long axis that weight is distributed (which partly depends on head width), and how flexible is the frame. On off-long-axis hits, with all other factors being equal, less weight (or less widely placed weight) in the racquet head allows more rotation around the racquet's long axis (torsion), because the racquet head has less mass on either side of the long axis to provide rotational inertia. Off-long-axis hits also put extra stress on the frame materials, and a more flexible frame twists out of shape more readily. Both reactions to the ball-racquet collision introduce unintended upward or downward tilt of the racquet face when the ball leaves the strings, with the turning due to lightness usually considerably greater than the twisting due to flexibility.
When the ball hits the racquet face off the long axis, the racquet loses some power, and the loss of power can either mitigate or exacerbate the effect of the tilted racquet face. If the ball hits above the long axis, causing an upward tilt, the loss of power will help to prevent your hitting long. If the ball hits below the long axis, causing a downward tilt, the loss of power will make it more likely that you'll hit the net.
The impact of the ball bends a more flexible frame backward farther as well, not just on off-long-axis hits, but on all hits, especially those closer to the tip. This introduces another variation in the angle of the racquet face when the ball leaves the strings, changing (slightly) the left-right direction of the ball instead of the up-down direction.
The above leads us to an important conclusion that's highly relevant to control: A stiffer racquet with more weight in its head is less likely to send the ball off at an unexpected angle.
Stiffness and weight, especially head weight, also have a major effect on power.