Depends on the shooter and load. The 44 Spl is probably more inherently accurate, all things considered, due to greater mass (momentum) of the bullets.
The 38 Special has been the preeminent center fire target load (especially in the 148 WC), for a good part of the 20th. Century. Paired with the great Colt & Smith & Wesson target revolvers of the time, it's still hard to beat.