Starts are versatile, and because their bolt on neck, they have more of a "twang" to thier sound, they're also pretty comfy too... they can sound bright and chirpy, they can also give a lovely hank marvin-esque sound...
Les pauls, great sustain, more tone due to thier glue in necks (i think anyway), they usually have 2 humbuckers, so really good for rock and blues, and also their shorter scale lengths the strings are looser and so they're good for bends..
Personally i like starts better for thier more versatile sounds, their longer scale lengths...
saying all of that, I'm actually biulding a guitar at the minute, that resembles a les paul more than a strat... except it's got a long scale length (slightly longer than a strat's scale length)...