Hello Aspirant,

Both IGNOU and Osmania University holds a good reputation and recognition in India hence  degrees obtained from the same will hold value. Here , you should take decision based on your future plan or requirements. It is to be decided based on your intention to whether get the degree through distance mode or regular mode. If you are expecting immediate career opportunities , even though distance programs holds value , common choice would be regular. If you are already working then correspondence/distance course would be convenient .The second  point to consider is that political Science is a much diverse and complicated field in comparison to public Administration. Public administration is a sub field of political science,so you should decide according to your needs. Also it is not permitted to do a a regular or distance course in another university while doing a course from IGNOU so the answer to your second question is no.

https://www.careers360.com/university/indira-gandhi-national-open-university-new-delhi

https://www.careers360.com/university/osmania-university-hyderabad

All the best