I'm not an expert in either, but my understanding is that ChiA-PET is generally a more powerful method in that (1) it allows you to probe long-distance interactions relevant to some protein of interest, (2) it involves ligation of known adapters containing Mme1 cut-sites, which are exploited to get fragments with both sides of an interaction separated by known sequence, and (3) you can use multiple adapter sequences with ChiA-PET (divide the initial cross-linked and sonicated sample into multiple tubes) to gauge how frequently false-positives are found. In my mind, points 1 and 3 are big selling points, but there may be other big differences. There's a nice visual comparison of the two in figure 4 of this review article.