blockchain webgame - use api or actual blockchain to build database?
Use a third-party API if the correctness or accuracy of the data is not important. When the financial data needs to be accurate, using a third-party API is slightly more dangerous because as an intermediary they can return whatever (possibly tainted) data to your service... selectively.

Naturally, weigh this against the costs of maintaining an active bitcoind node such as upgrades, sysadmin maintenance, security, etc. There may also be an option regarding simple payment verification if you do not require the entire blockchain.