For the latter group, the answer is Bidwell & Curran's paper "The Automorphism Group of a Split Metacyclic p-Group"
http://www.springerlink.com/content/c7324108h86282l1/Bidwell, J. N. S.; Curran, M. J., The automorphism group of a split metacyclic $p$-group, Arch. Math. 87, No. 6, 488–497 (2006). Zbl 1116.20016.