std::array<T, N> is an aggregate: it doesn't have any user-declared constructors, not even one taking a std::initializer_list. Initialization using braces is performed using aggregate initialization, a feature of C++ that was inherited from C.
The "old style" of aggregate initialization uses the =:
std::array<int, 4> y = { { 1, 2, 3, 4 } };
With this old style of aggregate initialization, extra braces may be elided, so this is equivalent to:
std::array<int, 4> y = { 1, 2, 3, 4 };
However, these extra braces may only be elided "in a declaration of the form T x = { a };" (C++11 §8.5.1/11), that is, when the old style = is used . This rule allowing brace elision does not apply for direct list initialization. A footnote here reads: "Braces cannot be elided in other uses of list-initialization."
There is a defect report concerning this restriction: CWG defect #1270. If the proposed resolution is adopted, brace elision will be allowed for other forms of list initialization, and the following will be well-formed:
std::array<int, 4> y{ 1, 2, 3, 4 };
(Hat tip to Ville Voutilainen for finding the defect report.)
Because std::vector offers a constructor that takes in a std::initializer_list<T>, while std::array has no constructors and the {1, 2, 3, 4} braced init-list is in fact not interpreted as a std::initializer_list, but aggregate initialization for the inner C-style array of std::array (that's where the second set of braces comes from: One for std::array, one for the inner C-style member array).