I've owned three SGs and played various LPs tho never owned one.
Hard to describe the difference but the SGs always seemed to sound more woody, maybe midrangy and a bit more honky/nasally is the best way to explain.
LPs had a fatter, fuller, creamier sound due in part to the thicker, mahogany body and maple cap construction.
I actually prefer the less refined, raspier sound of SGs as well as the lighter weight, tho they've been more inclined to neck dive than LPs for me.
Could I tell them apart blindfold? Yes if everything else in the set up was equal.
But listening to a band at gig volumes etc no i don't think I could tell you whether they were playing a V, Explorer, SG or Les Paul on sound alone.
Theyve all got a big slab of Gibson humbucker goodness. That's why we love them!