Advantages of Servo Systems over Stepper Systems:
The most significant difference between servo and stepper motion control systems is the use of feedback in servo controlled systems - that is there is a position encoder attached to the drive motor that reports the actual position of the motor shaft back to the controller. If there are any errors present, the servo controller may take corrective action to insure the motor reaches the proper position. Stepper controllers can only issue a move command and hope that the motor is capable of following it.  The presence of feedback in a servo controller system results in several immediate benefits:
Since servo systems know exactly where the motor is at all times, all step commands are executed. A complex series of motions may be reliably repeated over-and-over.

Torque at High Speeds:
Stepper motor torque falls off as motor speed increases due to electrical time constants and poor current utilization. Servo motors do not have this shortcoming and may generate full torque at high RPMs.  

Quiet - Smooth Operation:
Servo systems are inherently smooth due to their high encoder resolutions, typically at least ten times finer than the number of stepper motor positions per revolution. Acoustic noise is virtually nonexistent in servo systems since there is very little motor resonance.

Zero Holding Current:
Stepper motors must have relatively high currents applied to them at all times, even while stopped with little or no load. Servo systems meter out power only as required - proportional to the load torque applied to the motor.

Micro Stepping:
Stepper motors may increase their resolution by a process called micro stepping where currents are applied to the motor windings proportional to the desired position between normal steps. Repeatability and torque production are a problem for steppers in this mode of operation. Again, servo systems overcome this problem by supplying power as indicated by the on-shaft encoder.

High Efficiency, No Need to Over Specify the Motor or Power Supply:
The most common way to keep stepper motor systems from losing steps is to over design the system such that there is a very high probability that no steps will be lost due to high loads or friction. The usual design margin used by steppers is 200%!

Background on motor types:

Most motors used today are "induction" motors. Mechanical rotating force (torque) is generated by two electromagnetic fields--just like two like magnetic poles repel each other and two unlike magnetic poles attract each other. In the case of the induction motor, both the "poles" are electromagnetic. The stator (stationary part of the motor) consists of wires wound around a steel core. When current is fed into the windings of the stator it generates and electromagnetic field. This field "induces" another electric field in the rotor (rotating part of the motor which is made of "laminations held together in an aluminum casting). The two fields react (repel each other) and rotating force (rotating torque) is generated. The larger the motor (Either the OD or it's length) it will generate more torque. Conversely, the more power fed into the motor (voltage and current ) the higher the torque generated.

Induction motors are common because  their construction is extremely rugged. The motors are maintenance free and the manufacturing processes have been refined so that the costs are very low.  Induction motors have basic two problems;     First , they have low efficiency-most of the input energy is wasted in heat and it is difficult to control speed and position precisely.

There is another class of motors that address the efficiency and controllability issues. These motors, us permanent magnets in either the rotor or the stator. In sub-category called the brush type permanent magnet DC motors, the stator field is generated by permanent magnets. The rotor field is generated by the current flowing through the windings in a laminated steel core. DC current is fed into the windings through carbon brushes that ride on the commutator (or current reverser, which is a series of copper bars each ending in one of the copper wire coils of the rotor (referred to as the "armature").

The permanent magnet field makes brush motors more efficient than induction motors (since there is are not induction losses in the rotor) and also since the permanent magnet field is fixed, such motors are easier to control than induction motors. Changing the speed of a DC brush type motor is simply a matter of changing the input voltage--the speed of the motor is directly proportional to the applied voltage.

Another category of DC motors uses permanent magnets also but the magnets are in the rotor. Current is fed into the stator and the rotating action is generated not by the commutator and brushes (as in the case of a brush type permanent magnet motor) but by power electronic switches. For this reason, this category of motors is also referred to at times as a " electronically commutated motor" or simply an ECM. Since there are no brushes, this type of motor is also called a brushless DC motor. The advantages of brushless DC motors are numerous. Over induction motors the advantages are: much higher efficiency (since there are no losses as a result of the "induction" process such as in the case of an induction motor; much better controllability (the permanent magnet field is fixed and does not have the variation of an electro-magnetic field such as in the case of an induction motor. Lighter weight, faster response and higher speed are some of the other advantages of a brushless DC motor. There are a large number of variations in the types of motors--each variation is based upon the manner in which the rotating electro-magnetic field. 

C frame motors: 

These are induction motors with a stator in the form of a "C" Such are motors are inexpensive, terribly inefficient but are suitable where cost is paramount and efficiency is not.

Axial air-gap motors: 

In most of the motors described so far, the air gap between the rotor and the stator is radial--i.e. in a direction square with the motor shaft. Motors can be built with and axial air gap--the air gap is in line with the motor shaft. Such a design results in a "pan cake" style flat geometry, which may be suitable in some applications.

Slot less motors: 

Normally the current carrying copper wires are held in place by being wound in the slots of the stack of laminations of steel. Slot less motors do away with the steel slots and have their wires held together in a basket glued with suitable epoxies. The main advantage of such motors is that they have extremely smooth rotation since there are not slots to
cause bumpy motion as the rotor moves from slot to slot. The disadvantage is that it is difficult (and therefore potentially more expensive to build the wire wound baskets.

Switched Reluctance:

  These motors have toothed" stator and rotor. Such a Motors designs more efficient than an induction motor but less efficient than an permanent magnet brushless motor. However, it is less expensive than a permanent magnet brushless motor since there are no magnets in the rotor. The disadvantage of these motors is that the it is much more difficult to design the motor since it is "non-linear" characteristics and manufacturing tolerances required are very tight. Each motor has to be very precisely designed for the specific application.

Stepper Motor: