If its a choice between more power or less weight, I'd always pick less weight. The only time I'd take power would be if it was a top speed tune, in that case more power would be better.
Some high powered cars are less stable with less weight because it is easier to spin up the rear tyres but the same problem will occur if you added more power. All of these problems can be cured with a bit of a basic tuning, with GT6 you should never expect a car to feel and function the same when you start changing performance parts.