Imagine, that if the human race dies out (which it could very well do with the aid of nuclear war), that the last intelligent species is no longer in existence. Plus, what are the chances that they are more advanced than us. If we could find out how to travel the galaxy, or even the universe, what are the chances they could rival us?
No, learning we are alone in the universe would not be more terrifying than learning that we are not. In fact, neither would be terrifying. In one scenario, the human race is very much uniquely special, the only species to achieve sapience. In the other, we would find more like ourselves and become part of a larger community. Both are incredible to conceive.
Learning that we are the only planet within any universe that hosts living, communicable species would be quite satisfying, in addition to making us feel more safe. Knowing that there are no life forms in the universe that could threaten our existence would be peaceful and would put an end to the debate of greater life forms that could wipe us off of the planet.