I might be biased because I'm Polish, where the president is elected, and I hate the system compared to Germany or Italy.

A political head of state is not good imho, just ends up vetoing and doing politics instead of acting as a guardian of the constitution and institutions.

It's just a matter of "elect president from government's opposition and he's now emboldened to veto and block anything because he has popular mandate to do so".

Politicians electing the president seems a better option because they need to compromise on an individual that will allow any party to govern and be checked.