They are equivalent. I would expect the second to be faster, and it will cut memory by a factor of 4 since the same amount of memory is needed to store 1 bit integers as 4 bit integers (I think the smallest granularity supported, even by the relatively new integer types, is at least a byte).
As for the problem at hand, you'd check the ratio of 12s to 15s I guess.
As for equivalence in principle, one can convert the second representation to the first using IntegerDigits[...,2,4] and the first to the second using FromDigits[...,2].
