I have one CIC on my books, however, I only do the bookkeeping to TB - they have an accountant (that is a CIC specialist) that do their end of year accounts prep and submissions, Corporation Tax etc.
The CIC has the same obligations as a Ltd Co with Co House and HMRC etc, but with the client I have, the Accountant fills out an extra form that reports the various 'promises' that they have to make to the community, in order to meet the criteria of a CIC. That's one difference.
Another difference is that, although my client is the owner and a director, he's not allowed to take any dividends as all 'profits' are expected to be invested back into the company. I have put the word profit in inverted commas because they don't call it this - it is known as excess income, or anything but the word 'profit!
The way my client deals with this is that he's also self employed and invoices the CIC for his time - or obvioulsy he could be salaried if he chose to be.
Other than these few things - I don't notice any difference, but then like I said, I only do the in-year bookkeping, so I may not be fully aware of other things that go on perhaps. The end of year accounts charge is pretty low compared to other Limited Companies I have on my books, but whether this is an indication of just a good price, or that they have very littel else to do when my bookkeeping is so tidy for them ( ;-) ), I'm not sure.