Having operated both LAA permit and C of A aircraft I would say that the LAA permit is much cheaper. Mainly because of the reduced cost of paperwork and the ability to do work yourself signed off by an inspector when needed. The LAA does require detailed records of maintenance, with worksheets for all work done so ask to look at these and see if work done is thoroughly recorded. C of A will have the same.
The accident rate between both types is similar, there are scare stories with both.
With both types there is nothing to stop the unscrupulous owner doing some hidden bodge and not recording it. The only way to pick this up is a thorough inspection.
The most important thing is to decide what aircraft you want. In almost all cases this will determine whether its a LAA or CAA aircraft. ie there are hardly any types where the same type of aircraft can be LAA or CAA.
Then ask around, most of the types have extensive information available on the web. Then make sure you get advice from someone who knows the type.