In my experience ICs do not have specific sound characters. Most ICs are not even used for audio circuits. One could argue that if we go back to the earlier days of integrated circuits, they had performance limitations compared to similar circuits fabricated from discrete devices, that may have inferred a characteristic sound. Back in the not so good old days there were notable differences between different engineer's implementations using the same raw parts. Probably more so than today since ICs have done a lot of catching up since then. Modern IC devices today, are certainly linear, quiet, and powerful enough for 99.9% of audio applications. It is easier now for less skilled engineers to get good results.
The linearity and precision delivered by the new generation IC opamps is difficult to match in even a "cost no object" DOA design, due to the inherent benefits of integrated circuit device matching, thermal tracking, etc.
About the only intrinsic limitations of IC opamps, is that you can't easily incorporate a large value inductor into the input long tail pair, or operate from higher than nominal process voltages (40V or so). These limitations are not game stoppers or reasons to expect inferior sound quality.