They essentially do the same thing. I generally go for caster adjustments first because it’s a bigger swing. I use the front width to fine tune the feeling of the front end because you can adjust in small 5mm increments.
Both are going to alter the weight jacking of the kart and affect how the kart reacts to turn-in and then how long it keeps the inside rear wheel unloaded.
Wider front track = more weight jacking, stronger turn-in
More caster = more weight jacking, stronger turn-in
Getting too wide on the front can make the kart slower to respond to steering input. I prefer to adjust caster at this point instead as I feel like it affects the steering reaction less.
My theory is that you always want to run as little caster/as narrow a front end as possible while still getting the kart to turn in properly and lift the inside rear wheel. The more geometry you introduce to the kart, the more scrub you will get in the front end and the worse the kart will roll off the corner. That being said, you will almost always need SOME caster to get the kart to rotate.