List<T> is basically backed by an array which is usually bigger than the current number of items. The elements are put in an array, and a new array is created when the old one runs out of space. This is fast for access by index, but slow at removing or inserting elements within the list or at the start. Adding/removing entries at the end of the list is reasonably cheap.
LinkedList<T> is a doubly-linked list - each node knows its previous entry and its next one. This is fast for inserting after/before a particular node (or the head/tail), but slow at access by index.
LinkedList<T> will usually take more memory than
List<T> because it needs space for all those next/previous references - and the data will probably have less locality of reference, as each node is a separate object. On the other hand, a
List<T> can have a backing array which is much larger than its current needs.