compared to the discrete wavelet transform the Wavelet Packet transform essentially decomposes not only the low pass filtered part of a signal (the approximation coefficients) but also the high pass filtered part (the detail coefficients) yielding a higher frequency resolution even in higher frequencies.
unfortunately it's not that easy; it depends very much on the data and the task you have to accomplish which version of the wavelet transform is most appropiate for you. Probably you won't come through going more into detail of wavelets by yourself in order to decide which version is the best one.