John has given an example of why an ECU remap is better than a plug-in box.
An ECU remap interacts with all the engine feedback sensors - such as throttle position, load, airflow, rpm, and selected gear (auto only) - and integrates these signals into the ECU fuelling calculations. This results in increased power, nearly always better fuel consumption, and seems to be kinder to the engine or the environment.
The plug-in box can only react to the fuelling signals already calculated by the ECU, altering the exact time and duration of fuel injection. This does result in increased power, and either slightly better or slightly worse fuel consumption depending on circumstances.
The disadvantage of a remap is that, unless you have a laptop and the right cable, the remap is stuck in the ECU - you can't simply unplug it.
About 5 years ago, VW were running a team of 170bhp Golf TDI 1.9 in 24 hour endurance races in Germany and Holland, compared to the 115bhp TDI then on the streets. This extra power was courtesy of an ECU remap and a higher setting Turbo waste-gate pressure valve.
If the car manufacturer has increased the engine power, but kept the same gearbox and transmission components - then it should be perfectly OK to apply the same power increase via a remap or plug-in system.
If the car manufacturer made changes to the gearbox or transmission. then take lots of care. For instance, the reason the Mini D has the Getrag 6 speed gearbox, also fitted to the Cooper S, is because the standard 5 speed Cooper or Mini One gearbox won't handle the extra torque from the Diesel engine.
Robert