The richter scale is a measure of the amount of shaking experienced during an earthquake - not a measure of the actual amount of energy released during the quake - so it really doesn't tell you anything about the earthquake from a scientific perspective - shaking may vary depending on where the seismometer is located (more shaking would be experienced on sediments than on bedrock, for example - like if you compare a house built on Jelly to one on the table!) and also on the building within which the seismometer is held - the design, and how earthquake-proof it is, will affect the shaking experienced. Moment magnitude, on the other hand, is calculated from the amount of slip which has occured on the fault, and the area over which it has taken place (eg if 200 square metres of fault moved 10 metres or something) - and is therefore a much better measure of the actual size of the quake. The richter scale is still quite useful when dealing with the general public, however, as the numbers produced from the moment magnitude measurement are rather large and scary looking, where as richter scale is just like "4.5" etc...
Hope that helps