This is deep off season, so the day of the week will make little difference, and neither cathedral is going to be particularly crowded.
If these are day trips from London, then the train would be the far better solution for either city. Driving only makes sense if you are on your way somewhere else.
You need to check both websites closer to the time for any events happening which cause closures to the Cathedral for all or part of a day.
Both cities have extensive park and ride facilities to keep traffic out of the centre.
Also
During 2024 improvements are being made to the approach to the city around the Railway Station and Fisherton Street area. This includes temporary road diversions which may mean heavier than usual levels of traffic in the city centre at some times of the day.