As someone who owns 2 Gibson LP customs, 2 Epi LP Customs, and an Edwards......the Edwards is easily the best playing and most stable guitar of the 3. Like....it kind of pissed me off when I got it because it just feels THAT much better than my Gibson Les Paul customs in the playability dept.
That being said, my black 05 LP custom is probably the best sounding guitar I own. The Edwards sounds great, but it is not a total tone monster like the Gibson. Of course, that's my opinion/personal taste speaking, so take it with a grain of salt.
My Epi LP customs are ok. I have the Matt Heafy and the Silverburst inspired by Gibson models. The Heafy's fretwork is meh. I may have it pleck'd because otherwise, it's a great guitar with awesome features, and stays in tune very well.
The Silverburst is a project guitar. Bought it from GC used, it came with a bunch of sanding marks all over the finish from someone trying to dull the shine, looks like ass, but came with burstbuckers installed which was a big value add. I ended up getting the guitar for $100 after partial refund from GC and selling the BB's. Sweetwater is sponsoring a video for me to restore the guitar and deck it out with new pickups, nut, hardware and wiring harness, so I'm excited to see how it stacks up after the mods.