An inertia dyno such as the common dynojet measures power and torque via the acceleration of the roller. The roller itself is a mass equivalent relative to the vehicle being tested. It works great, but isn't adjustable.
A dyno with a brake, such as the mustang dyno that has an eddy current brake, can get away with a smaller roller, as it has a power absorption unit that can account for additional power through adjustable resistance. The main benefit is different testing methods available to use with tuning vehicles such as steady state testing, rpm field testing, and programed simulations.
The correction factors are generally used to compensate for different environmental factors such as temperature and humidity. This way vehicles can be relatively compared across the world, but the dynos do need to be calibrated due to variables such as friction forces from bearing wear.
Horsepower/torque numbers can have variances due to added load especially on turbo vehicles, but generally, the main change I've seen is where in the powerband its produced.
In my opinion, find a dyno that's local to you and use it every time so you can see the improvements for your ride from modifications you've done. If you want to compare numbers with others on a competitive side, then get together and run on the same dyno. For general comparisons, just use the same correction factor. Just my thoughts.