The two common transmission methods in many mechanical systems are Belt Drive System and Chain Drive System. Each of them has its advantages and disadvantages depending upon the specific needs of a particular application.

Belt Drive System

A belt drive system uses a belt to direct power between wheels, which may number more than two. The advantages include:

- Silence: With less noise produced by an action of a motion transmission.

- No need for lubrication: As it does not require oiling, it implies that the belt drive system reduces maintenance costs.

- Flexibility: It can be used on belts with different sizes and shapes to transfer power from one wheel to another.

Nevertheless, there are some demerits associated with belt drive systems as discussed below:

- Low efficiency: Due to slightly stretchy nature of belts, most belt drive systems tend to be less efficient than chain-driven ones.

- Likely to slip: When heavily loaded, the belt on such wheels can slip causing unsteady energy flow through them.

Chain Drive System

Chains pass energy from one gearwheel to another in chain drive systems. These benefits include:

- High efficiency: That results from large contact surface between the gear wheel and the chain that reduces slippage during movements.

- High load capacity: Can accommodate heavy loads in the presence of such forces resulting from different mechanical movements within a machine etc…

However, chain drives have several drawbacks as presented here:

- Requires lubrication: This requires regular lubrication hence adding up maintenance expenses pertaining this type of technology (chain drives).

- Produces loud sounds when running：therefore, it generates much noise when running.

In conclusion,Belt Drive Sustem and Chain Drive Sustem both have pros and cons for themselves.The choice depends on individual requirements like if you need a quiet low-maintanance system then choose Belt Drive System.However if you want a highly efficient system that can withstand heavy loads then Chain Drive System is better suited for this use. The most important factor to put into consideration while making the decision are specific application requirements and environmental conditions.