I'm wondering exactly what the difference is between a turbo exhaust manifold with an internal wastegate and one with an external wastegate, besides the obvious one is internal one is external explanation. also what are the ups and downs of each one and which one is the better choice.

 

Typically the externals will make more power partly because the wasted exhaust doesn't add to the backpressure in the exhaust system.They also give you the option of a boost controller rather than just the spring in an internal setup.The internal is usually quieter and simpler to install.
Glenn