In CB accounting, one also allocates to the consumer (= the country) the emissions released to make and (sometimes) transport its imports. This means that a country can deduct the emissions that it has released for its export products and services. After all, these are carried by the importing countries.
Production-based accounting (= PB) does not deal with inputs. PB is exclusively referring to emissions generated at the point of production, that is, emissions physically produced mainly through the combustion of fossil fuels (coal, natural gas, and oil) for energy and transportation within the jurisdiction of a given state. The international climate agreements so far are based on PB accounting. There is nothing wrong with that (because all emissions are covered) as long as a solution is found quickly for the bunker emissions (= international transport emissions), which are not covered anywhere up to now.
CB seems more equitable but according to most authors (e.g. Afionis et al) has no future as a mitigation instrument because (a) of data uncertainty and incompatibility, (b) because of the incompatibility of any policy focus on those kinds of emissions with the freedom of spending of citizens and with the international relations that prescribe unlimited (nondiscriminatory) access to each other's markets.