EDIT: I was partially correct. It seems Voyager can transmit at up to 1.4 kbps for certain things.[1]
[0]: https://space.stackexchange.com/questions/24338/how-to-calcu...
(Asked in the spirit of curiosity; I'm ignorant of radio physics).
The uplink and downlink are in different frequency bands, S-band (2-4ghz) for uplink and X-band (8-12ghz) for downlink and have different amounts of radio frequency bandwidth allocated.
Additionally, Voyager's High-gain antenna has a much narrower beamwidth in X-band at 0.5°, compared to 2.3° for S-band, though I have no idea if that's a factor.
The first is that the downlink is at a higher frequency (X-band, 8.4 GHz) so there is more available bandwidth and the beamwidth of the antenna is tighter at a higher frequency (i.e. the power is more focused). The uplink is at 2.3 GHz, but part of the advantage of the larger beamwidth is that you are able to command the spacecraft if there is an anomaly and it is the high gain antenna is more offpointed. There is also a low gain omnidirectional S-band antenna in case it is really offpointed.
Although the signals both come through the high gain antenna there are two different feeds for the X-band and S-band. If you take a look at the picture of the antenna on Wikipedia [0] you can see the X-band feed is the prime focus behind the subreflector. The S-band feed is mounted on the subreflector so its not seeing the optimally focused signal (which the lower frequencies are less sensitive to this overall loss of focus for the reasons above).
Generally a lot of spacecraft are designed with a much higher downlink to get science data down, but you only need a pretty small link to get commands up to the spacecraft.
[0] https://en.wikipedia.org/wiki/Voyager_1#Communication_system
Of course, this wouldn't help Voyager, but it would help similar modern projects, since we can throw billions more computing power at these kinds of projects, these days.