There is per se no specific advantage of buying an insurance policy from a Government Insurance company. You must get clarity on your needs, preferences, and find the product that suits them - that is all.
One important difference between Government Insurers and Private insurers is the way they operate.
Private players have centralized processing of service requests, claims, complaints, disputes, etc. All their services can be provided by local branches as well as by centralized service offices like Toll-Free, Email based service hubs.
Public sector companies are decentralized. All the communication, calls, decisions are taken by the local office. In case you move from your current city to another city, the policy will have to be transferred under a written request to a new branch. Even if you call them toll-free or write to them on Social media or an email to their head office, these service requests will be redirected to the branch or regional office for resolution.
The benefit of decentralization is that you can have a rapport or relationship with the local office (if they are responsive) and get your work done, issues resolved. There is no local relationship-based leverage possible in the Private sector because all the decisions or calls are either controlled through systems, processes, or through a central team.
Hope this answers your question. Do let us know if you have an