First of all do we need to clarify what we mean by politically appointed vs. permanent Civil Service. In each country there are to a certain degree posts in the Civil Service that are career posts to which you ascend by working the system without the need of political friends that would promote you. These posts are considered permanent. On the other hand you have to (in general) a lesser degree the top posts in administrations that are politically appointed. Whether this includes only the minister/secretary or whether it even includes more ranks in a given administration depends from country to country. These positions are to be considered politically appointed.
Now to the essence of the question. What arguments can be made in favour of, or against, these two models?
As there are no two models that are exactly the same but as they differ all by some degree it is impossible to say which one is clearly better than another, nonetheless can we argue about general, abstract, advantages and disadvantages.
The advantage of permanent Civil Service is that no major political decisions will be taken at the administration level so that the whole power lies in the hands of the elected members of government that give the instructions to be followed by the administrations. On the other hand can that also be considered a disadvantage as Civil servants have political opinions too and could thus block political action through their own inaction. This of course only if they disagree with the instructions.
Having a stronger emphasis on politically appointed officials lessens this problem but introduces the problem of major overhauls of whole administrations after each election. This diminishes the effectiveness of administrations because they regularly have to adapt to a new leadership.
The models differ by degree of political appointments and stronger emphasis on political appointments guarantee that political decisions are not blocked by senior staff but generate a lot of inefficiencies due to changes in leadership on each government change. More emphasis on career Civil Servants leads to more continuous administrations but risk the blocking of initiatives by Civil Servants.