If you're using buy links directly to the shopping cart on your affiliate website, you should consider customizing your order interface template, at least for the following reasons:
Increased trust - when shoppers are redirected to our payment interface, the vendor default template will be used. Some of the visitors may consider this untruthful and, thus, abandon the shopping process.
Control the shopping process - you know best (or at least you should have an idea of) what your audience's needs and website flow are. So, you can serve them the right things in the shopping cart and avoid issues like an inappropriate shopping cart template defined by the software vendor or any other changes in various stages of the shopping cart that might affect your conversion rate.
Market the products better - many say that the software vendor is in the best position to market its products. However, there are many examples that prove the opposite - affiliates having more success in selling products than the vendors, given the fact that, for example, they may address specific niches, local audiences and so on.
Optimize the shopping cart - give your customers contextual links to your website, recommend them other things or just focus on the buying process - whatever your optimization strategy is, you can put it into practice.