Neither, or both.

This is more a linguistics question in the field of contemporary and historical usage, but in the interests of fulfilling your question, let me talk about these terms for awhile.

Firstly, “Fatherland” and it’s cognates has a well established usage across European languages, especially Indo-European and Romance languages. You can see it, if you know Greek and Latin, in the forms πατρία and πατήρ/patria and pater. Anyway, ‘Fatherland’ is not really a common English term, and for many English speakers its associations are caught up in the emergence of the term Vaterland in propaganda associated with Nazi Germany. Thus, for English speakers, ‘Fatherland’ sounds like an echo of that ideology, even though Vaterland is not itself so definitively tied up in Nazism in the German Language, anymore than its cognates in other European languages are necessarily tied to nationalist ideas of that kind.

Several other countries and languages prefer to use feminine language/language forms, for their nation, most notably Russia, and the term Россия-Матушка, or ‘Mother Russia’. This personification of the nation as a woman is found even in languages that use patri-based terms. For example, even though Latin has patria, Roma is still a feminine form and the personification of Rome as a female entity also played a role in civic and national identity-discourse. I would suggest that personification of the nation as a mother figure has to do with the combination of traditional depictions of the ‘earth’ as feminine and the land/nation as the place that gives birth to a people.

To come back to English, neither of these is ‘more’ correct or appropriate, there does not seem to exist a longstanding tradition of embedding one of these concepts into the language more firmly than the other. “Mother Country” is used sometimes to refer to the UK by emigrants/descendants in colonial situations.

All of which is to say, neither or both could be viewed as appropriate. I hope this has been at least mildly informative and answered your question. Feel free to ask follow up questions if you’d like more historical/linguistic information.