As Long as it's a real ESP and not a LTD Eclipse you are better of with the eclipse... Gibson guitars are great but keep in mind that the studio is the lower end Gibson Les Paul while the Eclipse a high end Esp. The esp is heavier (which gives you a deeper/warmer sound) it is crafted better and it has the better hardware/woods. It should have a remarkably better tone than a Gibson Les Paul Studio.
If you want it to sound versitaile, then buy the Eclipse with Seymour Duncan Sh-4/sh-1 equipped and not the version with emg pickups.
In general you could say:
Gibson Les Pauls Studio < Esp Eclipse
Gibson Les Paul Standard > Esp Eclipse
Gibson Les Paul Custom > Any other guitar (imho)
I don't agree that the Custom beats the Reissues. I have an R8 and also two Studios. Also Studios are fine.
I would take a look at the new Standards. They have the long tenon like the reissues (that does give better sustain), and some other features, including a Plek'ed neck. Anyone who does not think Plek'ing is huge, has not played a Plek'ed neck (my R8 is Plek'ed, and it is a big deal). I don't have a problem with the chambered body, I will take that over weight relief holes as they did in the past. The Reissues have neither, they have solid bodies with no weight relief, using selected light mahogany. But I would really like one of the new Standards.
Actually I think the new Standards are a good deal. I would have expected a much higher price with those new features. Those the the features that in the past were reserved for the custom shop.
Tough choice, both great guitars..
I'd probably go for the Eclipse, as I like that better than a regular Les Paul Studio
My Les Paul Studio is kind of a special model, which are much better than your standard Studio, so I like that one as good as my Eclipse II..
Depends a bit on what style of music you play as well and what sound you want
Do you have a Premium? I have one of those, the top is really pretty. I like it. I got it used. I took the pickups off once, and noticed that the Maple top was quite thick. It was one of the early ones. I don't know if they make the Maple tops as thick on your basic studio. People often say they are lighter, which would indicate not. My old Premium Studio is pretty heavy, as heavy as my R8, 9.5 lbs.
I also have a Mahogany, that I got a good deal on ($600). It has an unusual sound, and Burstbuckers, so it was a good buy, I like it.