Well, it seems to me ArrayLists make it easier to expand the code later on both because they can grow and because they make using Generics easier. However, for multidimensional arrays, I find the readability of the code is better with standard arrays.
Anyway, are there some guidelines on when to use one or the other? For example, I’m about to return a table from a function (int[][]), but I was wondering if it wouldn’t be better to return a List<List<Integer>> or a List<int[]>.
Unless you have a strong reason otherwise, I’d recommend using Lists over arrays.
There are some specific cases where you will want to use an array (e.g. when you are implementing your own data structures, or when you are addressing a very specific performance requirement that you have profiled and identified as a bottleneck) but for general purposes Lists are more convenient and will offer you more flexibility in how you use them.
Where you are able to, I’d also recommend programming to the abstraction (List) rather than the concrete type (ArrayList). Again, this offers you flexibility if you decide to chenge the implementation details in the future.
To address your readability point: if you have a complex structure (e.g. ArrayList of HashMaps of ArrayLists) then consider either encapsulating this complexity within a class and/or creating some very clearly named functions to manipulate the structure.