When you're playing with a slide you'll notice that there is A LOT of treble in the tone. What I do when I play slide is try to take the treble away and get a nice smooth warm tone. The slide is going to give the notes plenty of clarity either way but a lot of times it'll make your tone sound too harsh and sharp. Use your neck pickup and maybe roll the treble knob back on the amp. A good piece of kit to have in any tone situation is an EQ... It will allow you to cut those high frequencies to compensate for the magnified trebles.
I use larger gauge strings on my slide guitar... which is a Mexi Fender Strat.
Most of the tone though comes from the hands, just like any other kind of guitar playing.