I tried PrestaShop. I found that-- just like Magento-- too many essential functions required a third-party module. And most PrestaShop modules cost money. But the biggest show-stopper for me when it came to PrestaShop was the fact that it doesn't allow partial shipments natively. The feature was requested by users as early as 2011, but it still hasn't been added. That should be core functionality. Period.

I'm afraid I'm going to have to stick with Magento. Thankfully, Magento 2 has become mature enough to consider it as an option.