I have an older Korean built Epiphone Les Paul Custom. It's well made and actually does have a Mahogany body & neck with a Flame Maple top & a Rosewood board. The problem with some Epiphone LPs is that the bodies are made out of mutiple blocks of Mahogany & Alder, which completely fucks up the tone. This is one reason I will never buy a painted Epi LP, at least with a finish that you can see through, you can see the wood that you're buying.
I can't speak to the newer Chinese built ones, because as soon as I found out tha they were being made there, I quit looking at Epiphone in general.
But in reality, if you look around, you can find used USA built Gibson LP Studios for around the same price as a Chinese Epi LP Custom.
As far as ESP/LTD Eclipse guitars go, they feel nothing like a Les Paul. IIRC, the scale length is the same, but the necks are shaped different, the bodies are thinner, and they don't sound the same. If you want a guitar that sounds like a Les Paul, you're either gonna have to buy a Les Paul, buy a guitar that's built like a Les Paul (Hamer, and a few others have made them over the years), or build one (such as www.precisionguitarkits.com's '59 kit).