what is the benefits of permissioned blockchain?
There are several 'benefits' (it depends on how you look at this). You can limit who can read the block or who can be the validator/miners and etc. By limiting the numbers of people who can read the block, the data on the blockchain will be 'safe' from third-parties, therefore only a few people will know it. The government would love this one. By limiting the number of validators, you can maximize your profits (assuming you own the blockchain and become one of the validators), so you'll get rich quickly. CMIIW.
How can i distinguish the difference on functions between centralized db and permissioned blockchain?
Not really sure get your point, you're talking what (technical) functions / features (like, block confirmation time?) available on a centralized database and permissioned blockchain? Read the source code or features, maybe?