Dual citizen here, 2 European passports. A lot of counties do not recognise dual citizenship of their own citizen, so you get a warning that even if you legitimately hold another citizenship (which they can’t do nothing about), it is not recognised in any way. The other country, which does acknowledge dual citizenship, tells me that the passport I travel abroad with is the consular service I may call upon: it is expressly forbidden to seek assistance from 2 nations over one problem when abroad. That’s all the limits I see / experience.