ArrayList and LinkedList are different, they different in speed but it depends on the operations and the overall usage you have of them... That's why there are different collections, not only they serve different purposes, but for similar purposes, they have different performances.
Some searches can better highlight the differences, but I will say, from memory, that LinkedList is good for insertion/removal of items (just change some links) while ArrayList must shift items. On the other hand, ArrayList is probably better for direct access to items, while both are similar for iteration.

Of course, both will do the "right thing" with regard to correctness after operations. For both, if you remove the first element, the next elements are shifted to the start.