Internal wastegates are cheap and take up less room. The downside is that all turbochargers were designed for automotive applications and those made with internal wastegates were not intended to control exhaust gas volumes as large as are produced at high rpm on a motorcycle engine.
The first problem is the minimum boost level.
With a car you could have the wastegate set for 8lbs and that boost level could be used in every gear. On a bike with a stock swing arm you can't use 8lbs in 1st gear and maybe not in 2nd. Few internal wastegates are capable of controlling boost below 8lbs because the internal passages are too small to vent the necessary exhaust gases away from the turbine. It is sometimes possible to port out the internal passages but the gain will likely be no more than a pound or two.
The second problem is what is called wastegate creep.
This is another problem caused by the smallish internal wastegate passages. As rpm and boost build the wastegate will open to limit the boost level but exhaust gas volume may reach a point at which boost continues to build even with the wastegate wide open because enough gases are still going through the turbine to do so.
External wastegates can be much larger than internal designs and can therefore vent more exhaust gas volume. With that ability it is possible to control the boost level to much lower levels than could be achieved with internal wastegates. This same greater venting ability also solves the boost creep problem.
So which do you need? If you can live with using less than full throttle in 1st and maybe 2nd gear and on the high-end boost doesn't creep higher than your desired max an internal wastegate will work just fine. I have used internal wastegates on two bikes with gear position based boost control since I can live with the lower gear issue and I run max boost levels high enough that creep isnt a problem. If however either of these points is a problem with your application then an external wastegate is the solution.
With either style if you need low boost for the lower gears and high boost (above the 15-20lb range) for the upper gears you may find that a single port wastegate (be it internal or external) cannot handle both. In that case you will need a two-port actuator and some type of boost controller so boost pressure can be used to increase spring pressure at high boost/rpm to keep the gate closed.
