One of the main differences between servo motors and stepper motors is that servo motors, by definition, run using a control loop and require feedback of some kind. A control loop uses feedback from the motor to help the motor get to a desired state (position, velocity, and so on). There are many different types of control loops. Generally, the PID (Proportional, Integral, Derivative) control loop is used for servo motors. For more information, see the related link, PID Controller: Theory and Practice.
When using a control loop such as PID, you may need to tune the servo motor. Tuning is the process of making a motor respond in a desirable way. Tuning a motor can be a very difficult and tedious process, but is also an advantage in that it lets the user have more control over the behavior of the motor. For more information about tuning servo motors see the related link, Basics of Tuning Servos Using PID.
Since servo motors have a control loop to check what state they are in, they are generally more reliable than stepper motors. When a stepper motor misses a step for any reason, there is no control loop to compensate in the move. The control loop in a servo motor is constantly checking to see if the motor is on the right path and, if it is not, it makes the necessary adjustments.
In general, servo motors run more smoothly than stepper motors except when microstepping is used. Also, as speed increases, the torque of the servo remains constant, making it better than the stepper at high speeds (usually above 1000 RPM). For information about how servo motors work see the related link below.
Servo Motor Overview