Advantages of the 4680 battery fall into two categories; production and vehicular use.
The #1 production benefit is the dry electrode process. It is hard to overstate how much better this is over making a slurry with solvents, then having to dry the electrode material and recover the solvents. The dry electrode process which Tesla acquired when they bought Maxwell Technologies is the primary reason why the 4680 production uses 1/10th the area compared to wet electrode battery production.
The other production advantage of the 4680 is the "tabless" design, without that tab in the way the automation process is faster and easier.
The continuous tab design is key to improved vehicular performance as well. The longer and narrower current path through that tiny tab limited the size of the cell. The 4680 continuous tab design can handle the current of a larger cell, and has a better thermal heat dissipation path for the inside layers of the jellroll, as well as generating less heat due to that shorter and wider current path.
Here you can see even though the 4680 has only 5x the energy, it can generate 6x the power.
That's a 20% increase in power for the same capacity. This bodes well for for increase performance overall, or at least better performance as lower states of charge.
I hope and expect that Tesla will increase the energy storage for the Model 3 and Model Y by about 10%, to about a 88-90 KWh capacity pack. This means we could easily have a 4680 3 or Y Performance model with 600 HP.
The larger battery reduces part count and allows using the can as a structural member leading to further weight savings.
Both the production methods and cell-to-structural-pack nature of the design lead to significant cost savings. I expect 4680 continuous tab designs to emerge a clear winner in the future.
Keep in mind that as they continue to make dry electrode process production gains you can expect to see this form factor with various chemistries like LiFePo, higher silicon, and someday solid state.