One of the algorithms used, called PRP (probable prime), which uses the reciprocal of Fermat's little theorem (a^(p-1)==1 mod p if p is prime) involves computing 3^p mod p (where p is a 110million bits number). This is called "modular exponentiation", and is done efficiently with FFTs (Fast Fourrier Transform, used to implement multiplication, thus squaring).
The FFT of 110Mbits can be implemented efficiently on GPUs. The key for keeping the hot data in GPU registers or caches is "locality of data access". Although the FFT algorithm is non-local by excellence (has a tendency to access all the data all the time), it can be split into "blocks" which have a smaller hot-data size. And this allows efficient GPU implementations.
The problem with R49081 may be that it's a small number, thus hard to fill all the processing units of the GPU with the amount of parallel work the algo offers at this size. Another problem may be that the algorithm involving eliptic-curves is more complex, thus more work is needed to express it in GPU terms.