The Pioneer and the Voyager probes are controlled in different ways.
Pioneer was spin-stabilized. By spinning the craft, it could act like a gyroscope and maintain the antenna pointing at the earth over long periods of time without using any thrusters.
Voyager does not spin. Instead it uses (small) thrusters to change the attitude of the platform as needed.
The big difference here is that without the gyroscopic stability, Voyager's attitude cannot be held in any direction with exactly zero error. The residual error is corrected with thruster firings. These firings affect not only the attitude of the probe, but also the momentum. Where Pioneer could spend long stretches of time drifting, Voyager is thrusting much more frequently. These firings would obscure any attempt to see a similar pattern in how it is moving.
New Horizons spent some time travelling with spin stabilization as well, but according to this answer on the Space stackexchange, precise tracking was not performed so there's no comparable data to look at.