Strats tend to have a cool thwaakk sound when you are hitting individual strings hard for heavy riffs. Les Pauls don't do that because the sound is a bit too creamy. However, with the right distortion, you can scare the bejeesus out of people with a massive Paul tone. I learned on a Strat neck, and it's width made certain solo techniques a real challenge, whereas they are much easier on the slimmer Paul necks.
I can't choose between the two without the song for which it's used. For cold steel metal or late night boogie, I pick a Strat. For witches brew doom metal or fun, beer-soaked hijinx, I'll take a Paul.