Crosstalk depends on the surrounding scenarios (meaning what's happening around). It can both degrade as well as improve the delay of a particular net. But most often we are more concerned upon the ones which degrade.
It affects the transition time of the signal, which is directly related to the upcoming cell's delay. The cell delay increases and hence can cause huge setup violation. You can separate transition / delay caused by cross talk. They are known as delta-transition and cross-talk delta delay.
We usually, keep 2x or 3x spacing between two different clock net shapes and also shield them. It is done to reduce the cross-talk.
To answer to your question precisely, it can affect both. But we are concerned (I'm not saying we need not fix hold. If we fail to fix hold, the design won't function at all) more on the performance of a design (setup) than hold. Unless most of the hold violations are due to crosstalk, we just fix hold by adding a delay cell.