There isn’t a hard set rule. Kart tuning is conditional. GENERALLY SPEAKING, a softer axle frees up a kart and a harder axle tightens up a kart. There are a ton of other variables to consider though. This is because the soft axle unloads and flexes more easily, causing the kart to lift the inside rear wheel and rotate better and a stiffer axle does the opposite.
However, you need to look at WHY your kart is handling poorly in a given situation. It’s very common to have a kart react similarly for two different (and often opposite) handling shortcomings.
There is a tuning “window” where the kart will work well in. Going outside this tuning window will result in the kart responding strangely to adjustments.
Too soft of an axle can cause the kart to overflex on turn-in, making the outside rear tire lose traction. This causes the kart to either slide or just sit flat and bog as the inside rear wheel drops down. A lower horsepower class like Yamaha usually has the kart just sit flat and bog in these situations because there isn’t the power of a TaG or Shifter to powerslide the kart when it goes flat.
Too stiff of an axle can cause a similar feel. If the axle is too stiff, the kart will never really lift the inside rear and will drag the tire on the track, causing a bog as the kart binds up around the corner.
In both the situations, it’s possible to have the kart bog and sit flat, even though you are using a hard axle in one scenario and a soft axle in the other. Selecting the correct axle for each situation relies on the driver to accurately diagnose whether the kart is lifting the inside rear too hard and therefore setting it down as the tires is overloaded, or if the axle isn’t lifting hard enough and is setting down early because there isn’t enough flex in the axle.
Axle tuning is one of the biggest changes you can make in a kart. My advice is to stay on the medium axle as long as you can and use the other adjustments in the kart first. Once you’ve exhausted your tuning options, then start looking at axle changes. Usually you don’t need to change axles unless you’re on a track that is gripping up significantly.
For hubs, it’s a similar theory (shorter = softer = less grip, longer = stiffer = more grip) but you have to keep in mind you are only changing the stiffness on the ends of the axle. As a driver, I personally never change hubs because I think it alters the way the tire interacts with the track surface and I don’t like the way it feels.
Like every adjustment in karting, choosing the right hub or axle for a situation is a balance. You need to find the right axle that is going to give you enough lift to rotate the kart but not too much that it will overload the outside tire. This can seem like an impossibility to figure out when the track is constantly changing session to session but eventually you will be able to feel what the kart needs and predict what it will need next session.