Difference between compressive sensing and DCT-based compression?
Comparing compressive sensing and traditional compression is a complicated task. Even  comparing two compression algorithms. 

One the one hand you have compression ratios, making sure the bits sent can be decompressed without other hidden bits. On the other hand, error measurements, rarely perfectly matched to the actual meaningful distorsions. [EDIT] Standard SSIM or NMSE are not well adapted to sparse signal.

Then, knowing the range over which one algorithm is better than the other is important, because one can be better at low-rates, the other at high-rates. There is rarely a free lunch in compression.

From a very mundane point of view, if you are in a compression range where the signal is not "sparse" enough (with respect to some basis) and the CS quantization is not really taken into account, yet sufficiently harmonic, it is well understandable that a DCT-like engineered algorithm can do better than a CS method if the CS theoretical conditions are not fulfilled.