they both use '57 classic Alnico-V pick ups, and are made of mahogany, but they are bound to sound slightly different.
im guessing they prolly sound pretty closely to the same, but id take the lp. sg's are known be a little... "thinnly" made
The les paul will be heavier, and the fret access wont anywhere near as good as the sg. tonally the les paul will have a meatier, thicker tone while the sg will have a more bitey tone.
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They would be almost identical. They're epiphone, so they automatically aren't at the top of my list, but they are just a shell around the same wiring. They are generic knockoffs of really expensive guitars, and neither of which sounds or plays good. it all depends on what kind of music you play. If you love slash and gNr, which almost everyone on this site does, then these guitars will sound okay to you, not great, but okay. You get what you pay for. If you play metal, i suggest a jackson, if you play, blues or rock or classic rock, i suggest a fender stratocaster, because a telecaster is the single ugliest creation in existence, no matter how pretty those single coil pickups sound.
well i play lots of stuff, from metallica to zeppelin to acdc.

however i do not want to spend as much as it would cost to get an actual gibson, and from what ive been told these epiphones do the job rather well.

i like both styles so im unsure which to get, so i figured id ask if there was a diff and maybe that would make the decision for me. =)

thx for all the replies so far!