What is better for 9 days staying in Shanghai? to buy Public Transportaion Card?

Yes, 9 days are really a long time stay, and an transportation card will help a lot if you travel by public transport like bus and subway. For 9 days, you are suggested to top up around CNY150. With that, you can also get a discount by bus and subway.

Therefore, you do not need to buy the three day metro pass, which is a bit more troublesome than transportation card, and the pass can only be used in subway, bot not on public bus.