Obviously, a direct database access will always be faster in simple scenarios.
With a WebService, you gain flexibility :
- plug-in a different implementation,
- when several applications need access to the same data, make one responsible for that data, and have the other one access it through a WebService : you will have no data lag between the two ; and you can keep often-accessed data in memory in that application, instead of using the database to communicate between applications....
Given your context of responsiveness (with possibly a problem with the other team), I would try to go the direct database access route, unless several applications need to share the data...