G'day Mate,
It really depends on what sort of plane it is, a pattern type aircraft, should fly the same when trimmed for full power as it does for 1/2 power, BUT a trainer is usually trimmed for straight & level flight at around 1/2 throttle, so that adding power will induce a slight climb, very helpful while learning landing approaches. So it all depends on the plane in question.
What sort of plane are we referring to here Kostas?