You are really talking a Chevy or Ford kind of question. People will fight to the death over which is better, Fender or Gibson. I owned several Les Pauls and Strats (nothing more recent than mid-80s models) as well as an Epiphone solid body.
First thing, what kind of music will you be playing? You want a classic rock sound, plug a Les Paul into some Marshalls. You can probably get the same sound from an Epiphone. You want more of a blues sound, go with the Strat. I could go on and on… I kept both my Strat and my Paul on stage, working with both during sets. The Epiphone that I had (can’t remember the model) was lighter than the Paul, so it did not have the same wonderful resonance you get with the Pauls.
IF you get an older Strat, I’d recommend getting it rewired, having the control cavity painted with metallic paint – they do like to hum and buzz if the wiring is a bit old, especially if you playing in a venue where the stage electrics are not well grounded.