Originally they made their containers because the standard library implementation was broken or incomplete on many platforms they supported. These days that's not such an issue, but avoiding the standard types allows them to make stronger binary compatibility guarantees.

I think it's a rather nice supplement to the STL. Their containers are optimized quite differently. For instance, all the Qt containers are copy-on-write.

Also, note that QList is not a linked list. QLinkedList is the counterpart to std::list.