Can someone help me understand an ongoing question I have not yet been able to crack?
It's a fairly generic question, so we'll struggle to provide anything meaningful... but when has that ever stopped us?
How are you assessing the backlinks? Most tools are notoriously inaccurate (compare the data from whatever tool you're using to a site you're in control of [and have more accurate data for, e.g. WMT, GA, etc.] and compare the results, you might be surprised at the differences). This could be part of the problem giving you an inaccurate picture of the authority of the sites in question.
From your previous posts, I'm assuming you've a firm grasp on factors like the relevance and theme of the links, so you're considering this when reviewing the sites. There's always an outside chance that there's a penalty at play, but I'd assume you'd have spotted this if it were the case.
Remember to take an holistic approach to it, look beyond the backlinks alone and compare citations/mentions/links from social media activity. If they're engaging well with the users (or users are happily sharing the content even without SMM activity by the sites), this is one area that might be partly relevant.
If the sites in question have been around longer than your client sites, they may have built up a strong historic CTR which will take some time for your client to achieve. This is the most likely reason, but again due to the lack of information it's very difficult to say for sure.