Well, being DCT-based isn't that important, but they are all still block-based transforms. It doesn't help that all wavelet codecs have failed, because video researchers only test with PSNR and not with human subjects.
H.264 doesn't use the DCT, but still uses the same size macroblocks, which is what made it unsuitable for very high-res video. HEVC uses up to 32x32 sized transforms.
H264's transform is integer a DCT approximation— optimized to only use small multiplies and shifts—, some may say that its far enough that it ought not be called a DCT anymore, though at least after correcting for scaling I wouldn't agree. In any case, it shares DCT's advantages and disadvantages.
H.264 doesn't use the DCT, but still uses the same size macroblocks, which is what made it unsuitable for very high-res video. HEVC uses up to 32x32 sized transforms.