I've used both and I prefer the live LCD for landscape photography, hands down.
As implemented on my current camera (Sony 717) the live LCD displays a live histogram, 100% coverage, continuous DOF preview, displays a bunch of shot info when I want, tilts up and down, displays the "sensor view" of the image (IE I can see the scene dynamic range on the LCD and see what areas are dark and light) and, best of all the image looks like the final product much more than a viewfinder (which to me is more like looking through a telescope). It's just amazing to be able to shoot and review on a tripod without having to crouch down / bend over / peer through a cramped viewfinder, then switch to the LCD for review, switch back and reframe and reshoot, etc. None of that dim DOF preview button nonsense either.
Yes there are some downsides for sure, but the overall working methodology is, IMO, far superior for my landscape photography work.
I'm hoping that someone comes out with a premium SLR system with live preview instead of a mirror. Maybe Sony will release a 20 MP 4/3 system camera.