Personally I feel that Prestashop has a bit of an old fashioned, convoluted checkout process, and the fact that the developers have ignored community requests for years to implement a more customer and conversion friendly checkout process to me says a lot about the developers mindset with respect to UX.
Actually, I’m going to have to eat my words, as an email has just landed in my inbox saying that one of the new features in their new alpha release… is one page checkout!
Magento is a modern, feature rich alternative, but can be difficult to develop for and requires good hosting. Opencart is worth a look too. If you don’t mind paying for a licence then trading eye is good.