External wastegates are used in most cases when you are having trouble controlling boost with an internal gate (meaning you are making more power, flowing more air, etc. than the small internal gate can handle). At this point people upgrade to external gates so they can again control the boost level.
There is no preset HP level where an external is needed as there are tons of variables involved. The main ones are boost pressure and exhaust backpressure.
Also, external gates still don't allow you to easily change your boost levels. You either need an adjustable boost controller (like you use with an internal as well) or you have to change the spring in the external to get a new PSI.
The 38mm, etc. refers to the size of the valve inside the wastegate. Basically, the larger the gate, the more air it will flow and the more power it will support on the same engine.