I know in system testing we have top-down integration, and bottom-up integration. But what is the best to use?

Bottom up is Advantageous if major flaws occur toward the bottom of the program.Test conditions are easier to create.Observation of test results is easier.

It exactly depends on your projects but I go for Bottom up

both are used depanding upon the project

Both Top-down and bottom- up approach of integration testing is used when some modules of the program are not yet integrated or is under development. In order to proceed with testing, temporary replacement modules are created that simulate the behavior of those ‘missing’ modules. The substitute for called module is termed ‘STUB’ and the calling module is called ‘DRIVER’.

Although Stub modules may appear simpler, they turn out to be complicated than expected. Hence test conditions and observations could be tedious to draw and analyze. However, each has its own pros and cons. In most cases, one approach takes priority over the other depending on the flow of execution.