If you are going to compare countries you have to do it per capita because the environment does not care about arbitrary political boundaries.
If you allocate allowed emissions per country instead of per capita, with each country getting a 1/N share of the Earth's total allowed CO2 emissions where N is the number of countries, then a country that is feeling constrained by that could split into two countries. Everyone's new share is 1/(N+1) but the former residents of the pre-split country now get to individually emit almost twice as much without putting their new country over its quota.
Of course other countries will figure out that trick too. In the limit it reduces to a world of 8 billion countries each with 1 person, and then is indistinguishable from per capita allocation.