The result would depend on cars, but an automatic transmission has an edge over manual transmission in acceleration in lower range because of the torque multiplification benefit given by the the torque converter. The presence of torque converter though, causes it to fall back in higher speed acceleration.
See the graph I made:
Starting from 0. the time it takes to get to speed on x axis.
pic
See the graph I made:
Starting from 0. the time it takes to get to speed on x axis.
pic