The difference is in how the plastic is colored. In the past, batches of each color were ordered in set colored pellets and molded into bricks. Now milky-white semi-transparent pellets (the basic color of abs) have color added to them during the molding process. It is much like having a paint color mixed for you at a hardware store. Several problems with bricks have occurred in the past few years. Bricks without enough base color are partially translucent. Heat and the size of the element effects the final color. This is why a dark blue 1x1 plate is much darker than a 1x8 dark blue brick. Certain colors such as white, light bley, dark bley, etc are often not consistent.
Why did LEGO make the change? My opinion is that it allows them to always have the colors they need, speeds up the production process, and reduces operating costs. Production of a set is not held up if they are low on color x pellets. Unfortunately, I do believe the old process usually had more consistent colors. Even in the past, colors did not always match (especially red) and hues changed slightly from year to year. Color changes where not as noticeable as they are today.