Here is a situation where they do not return the same result. By the way, you use APPLY only when you need to match previous tables / subqueries with the following.
SELECT x.x, y.x y
FROM (select [x] = 1) x
OUTER APPLY (select [x] = 1 where x.x is null) y
1, null
SELECT x.x, y.x y
FROM (select [x] = 1) x
CROSS APPLY (select [x] = 1 where x.x is null) y
(empty result set)
- ,