Split 32-bit LFSR into two 16-bit LFSR which xor to same sequence
If a given 64-bit sequence is known to be the bit-by-bit XOR sum of
the outputs of two 16-bit LFSRs, then the degree-32 LFSR feedback polynomial
found by the Berlekamp-Massey algorithm is indeed the product of the
(16-bit) feedback polynomials of the two 16-bit LFSRs, and as @poncho said, 
you need to factor the degree-32 polynomial into two 16-degree polynomials.
But, be aware that while this is guaranteed to work when the two 16-degree
polynomials are irreducible, there can be issues if the two 16-degree
polynomials are not irreducible or are not relatively prime. For example,
it might be that the Berlekamp-Massey algorithm (which finds the shortest
LFSR that will generate a given sequence) might give you an LFSR of length
less than 32 when the algorithm is applied to the 64-bit sequence.