Don't let wavelet vs DCT fool you. That's not the hard part of making a scalable video codec, and you can drop subbands from DCT too if you code the coefficients in the right order.

For compressing an individual image, wavelets provide automatic scalability: you can downscale by a power of 2 by dropping some subbands without recompressing. But that isn't sufficient for video. If you just downscale each frame, that essentially introduces intermediate rounding in the motion compensation process, and that rounding quickly accumulates to a very ugly distortion.

H.264 has an extension called SVC which addresses such scalability. SVC isn't widely implemented because it's recent and complex (as if H.264 weren't complex enough already), but it at least in theory works. On the other hand, Dirac does not even in principle support scalability.