As an owner of both a Gibson Les Paul Custom and a Gibson Les Paul Studio, I can concur with what eSGEe said.
However, in many cases the Studios have the same electronics and pickups as the more expensive Les Pauls. The original idea behind the Studio was to make a Les Paul that was as fully capable as it's more expensive cousins, but at a lower cost. Hence, the name "Studio." The marketing idea being this would be a good guitar for a studio, where looks don't matter as much as performance.
My Studio lacks nothing on my Custom, from the standpoint of playability, comfort, or performance.
I assembled my Studio from a husk, but the main differences really come down to the decorative and cosmetic features. There may be some structural differences. For example, my Studio is heavily chambered, whereas my Custom is not. Both are 2007 models. I don't know what kind of chambering they do today.
If you're looking for an LP, but don't want to drop the money on a Custom, a Studio will do very well for you. I really like mine.