In a CDD, you will be supporting an investor decision on whether to buy or not a company, usually by providing an assessment on the market that will be translated into the investment business plan (i.e., help provide specific lines on the business plan usually related to growth, segmentation, margin targets, etc.) also providing supporting evidence (research, expert interviews) and qualitative support.
The objective may not only be to assess the market where the company currently is, but actually to support the investment thesis (e.g. can they successfully expand to segment X, or market Y?) and assess key market risks (how much market share is at risk if xyz happens?).
You may also be working to calculate potential synergies (and one again, try to find evidence to support any assumptions made in the business model).
The work is, in my opinion, quite exciting and intellectually challenging. You have to learn a lot about a new market very fast, and you learn a lot about business models and how value is created.
Regarding skillset, you need a spike on analytical and structuring capability for this (and a good degree of authonomy). But client management skills don't need to be as sharp.
The downside is that projects are usually 3 week long given the time alloted in the deal process by the sellers. So you need to be super fast on everything. Is very very intensive, with long hours and a lot of crunch time, and you work from the office. So these are the 4 differences vs. regular “strategy” project work: longer hours, short project, no travelling, limited client interaction.