There are several advantages that stem from the fact that the Lamprey is an absolute encoder, whereas the Neo’s encoder is relative. As Lipstick stated, it helps account for backlash.
Beyond that though, one major problem with relative encoders is that they reset to position 0 when they power off. With most use cases, this is fine. Manipulators are typically in a known position when the robot starts anyway, and you don’t care about position so much as rotations in terms of driving. However, with something like swerve, your starting position is crucial and can be anywhere. There are ways to auto-zero on initialization (hall sensors), but that adds an additional level of both cost and complexity. Using an absolute encoder, such as the Lamprey, solves that for you.
Finally, absolute encoders typically have higher resolutions than relative encoders. This would only matter in the most complex of situations, but it’s still worth noting if you ever run into a resolution problem.
Another thing to note, the original design took advantage of a potentiometer that acted as a pseudo-encoder, rather than using exclusively the neo encoder. The only problem with this is that most potentiometers are not capable of continuous rotation, so it would force you to sometimes take the long way to any given module state.