Spur Gears have straight teeths. While Helical Gears have tooths crossed at an angle.
Spur Gears are very noisy and Helical Gears have greater load capacity than the Spur Gear of same size. This is because in Spur Gears take the entire load in the tooth whereas the Helical Gears distributes the same load on to the shaft hence the gear tooth itself takes less load than a Spur Gear of same size.
The teeth of Helical Gears are not parallel to the Gear axis; they are set at an angle. Since the surface over which the teeth are made is cylindrical, the teeth take the shape of a helix.
Advantages of the Helical Gear
Silent operation: In a helical gear train, the teeth engage a little at a time rather than the entire face at once. This causes less noisy power transfer in case of Helical Gears.
Non-parallel shaft: Helical Gears can be used for transferring power between non parallel shafts. Though you have to compromise on efficiency in this case.
Strength: For same tooth size (module) and equivalent width, Helical Gears can handle more load than Spur Gears because the Helical Gear tooth is effectively larger since it is diagonally positioned.
Helical Gear application
If noise is the main design criteria and you can compromise on power, you should go for Helical Gear. Helical Gears normally used for high speed, high power mechanical systems.
Example: Car gear box, machine tools etc.
Spur and Helical Gears are mostly used all around. You should go for Spur Gear for simplicity and efficiency. On the other hand Helical Gear should be considered for smooth high power applications.