With the right mix of suspension componenets and correct alignment, there is no reason your old car shouldn't feel as stable as your new car at speed, regardless of horsepower. Granted, the higher numbers will allow you to override traction at will if you chose so, but part of being a good driver is knowing your machine and its capabilities.
Things like efi adn computer managment systems have made it possible to run higher horsepower numbers without dealing with the associated headaches of high idle speeds and unburned fuel mixtures. A big cammed, over carb 400 horse motor can be a bigger painto live with than a 700 horse, forced inducted, efi mill. There are other parameters to it than just plain horsepower levels.