The answer, in a nutshell, is "better simulation of the actual transport environment".
Fixed displacement vibration has been around for over 60 years, and was the first type of vibration ever used for packaged-product testing. In reality, it was essentially the only type of vibration that could be practically supported by technology of the time (electric motor, belts or chains, eccentric cams). While still widely used, today it is mostly considered an "entry-level" or "simplified" approach - ISTA calls it a "Non-Simulation" test (ref ISTA 1-Series), and ASTM often uses the terminology "repetitive shock", not vibration (ref ASTM D999). Its advantage is that the equipment is inexpensive and the tests are simple. But its disadvantage is that it doesn't really simulate the transport vibration environment. It can certainly "beat up" a package and cause damage, but in many situations lab results do not correlate well with actual field performance.
A fixed displacement vibration test is run at nominally 4.5 Hz, where the test item just begins to "bounce" on the machine's table. It is easily observed and intuitively obvious that this does not mimic the motion of a transport vehicle. True, there is some intermittent "bouncing" of lading during transport, but transport is much more complex than simply a long interval of constant-frequency, constant-amplitude, and low-level shocks. Vibration frequencies in actual transport range from at least 3 to 100 Hz, and for the last 25 years or more the motion has been recognized as random, not periodic, in nature.
Literally thousands of field measurements and compilations now permit packaging engineers to accurately characterize the transport vibration environment in terms of random vibration PSD (power spectral density) profiles. Different shapes and intensities of these profiles differentiate various vehicles, road/trailer/air speed, lading, and other vibration conditions. With random vibration, it is possible not only to create meaningful laboratory simulations of generalized road, rail and air transport, but to be quite specific if desired - PSDs are available for "truck transport in China", "rail TOFC", "parcel delivery van", "jet aircraft", and many others (ref ISTA Project 4AB).
Now more than ever it is important to minimize the amount of packaging, investigate alternative configurations, try new materials, etc. But the packages must nonetheless still properly perform their intended functions. Accurate random vibration simulations support accurate package designs, making possible economies and efficiencies which cannot be realized using older methods.