What’s the difference between this product and the leather conditioner offered in the “cobbler’s choice essential leather kit”?

The Cobbler's Choice Leather Conditioner and Leather Cream are very similar. They consist of the same ingredients and both restore leather, but the Leather Cream has a higher concentration of Triple Filtered Beeswax, which gives the formula a semi-thick texture. Due to the higher content of Triple Filtered Beeswax, the Leather Cream also creates an even stronger waterproof barrier over the leathers surface, but does requires more time to dry. When considering these two products, it comes down to the users preference, as some users like to use semi-thick cream while others prefer oil-based conditioners when conditioning their leather.

Can this be used with vegan leather shoes?

Vegan leather is not leather. It's a way of churching up fake leather. They used to (some still do) call it faux leather knowing that sounds better than fake plastic trash for people who can't afford quality goods, and before that they called it pleather (plastic leather). Now that veganism is the liberal trend they can market it to sound even better. You can legit find better quality products/materials at the dollar store.

Will this work.on oiled leather?

I believe it should if it isn’t a suede finish but I cannot say with 100% certainty that it will. This is an oily type cream that works well on all regular leather shoes and boots to makeup them moist and protected but again I would not apply it to anything made of suede.