I think DWT is wavelet tree decomposition while wavedec2 is wavelet packet decomposition.
the wavelet packet analysis is similar to the DWT with the only difference that in addition to the decomposition of the wavelet approximation component at each level, the wavelet detail component is also decomposed to obtain its own approximation and detail components as shown in Figure2.the wavelet packet analysis provides better control of frequency resolution for the decomposition of the signal in contrast with DWT.