Thus far, nobody seems to have addressed the memory footprint of each of these lists besides the general consensus that a LinkedList is "lots more" than an ArrayList so I did some number crunching to demonstrate exactly how much both lists take up for N null references.
Since references are either 32 or 64 bits (even when null) on their relative systems, I have included 4 sets of data for 32 and 64 bit LinkedLists and ArrayLists.
Note: The sizes shown for the ArrayList lines are for trimmed lists - In practice, the capacity of the backing array in an ArrayList is generally larger than its current element count.
Note 2:(thanks BeeOnRope) As CompressedOops is default now from mid JDK6 and up, the values below for 64-bit machines will basically match their 32-bit counterparts, unless of course you specifically turn it off.
The result clearly shows that LinkedList is a whole lot more than ArrayList, especially with a very high element count. If memory is a factor, steer clear of LinkedLists.
The formulas I used follow, let me know if I have done anything wrong and I will fix it up. 'b' is either 4 or 8 for 32 or 64 bit systems, and 'n' is the number of elements. Note the reason for the mods is because all objects in java will take up a multiple of 8 bytes space regardless of whether it is all used or not.
ArrayList:
ArrayList object header + size integer + modCount integer + array reference + (array oject header + b * n) + MOD(array oject, 8) + MOD(ArrayList object, 8) == 8 + 4 + 4 + b + (12 + b * n) + MOD(12 + b * n, 8) + MOD(8 + 4 + 4 + b + (12 + b * n) + MOD(12 + b * n, 8), 8)
LinkedList:
LinkedList object header + size integer + modCount integer + reference to header + reference to footer + (node object overhead + reference to previous element + reference to next element + reference to element) * n) + MOD(node object, 8) * n + MOD(LinkedList object, 8) == 8 + 4 + 4 + 2 * b + (8 + 3 * b) * n + MOD(8 + 3 * b, 8) * n + MOD(8 + 4 + 4 + 2 * b + (8 + 3 * b) * n + MOD(8 + 3 * b, 8) * n, 8)