I'll weigh in a bit here.
Flight characteristics (VEZ compared to LEZ): Similar, but the LEZ has better harmony between pitch and roll - the VEZ is a little more sensitive in pitch, but just an aspect that one gets used to. Nothing I would write home about, unless you are ham-fisted and try to fly the airplane with your whole arm. The VariEze is a little hotter on landing, but the addition of trailing edge fences does a fair bit to knock off some knots required for approach and landing.
Useful load:
By-the-book, the LEZ standard max gross is 1325 pounds, with allowance to go to 1420 or 1425 with limitations (See Page 39 of the LEZ Owner's manual in the Downloads section of this website). The VariEze, by-the-book, and assuming correctly-built sparcaps & wing fitting interfaces (one does not know this unless they built the airplane, and built up the sparcaps and shear webs in stages like I did), is limted to 1050 pounds, and 1110 pounds max over-gross (with similar limitations as the LEZ). Rutan recommended tighter limitations on VariEzes (lower max g limits at +2.5 gs) based on forensic examination of a VariEze that had "swelled" sparcaps immediately adjacent to the wing fitting .125 inch plates.
My Eze is 617 pounds empty, and by-the-book, I have an almost 500 pound useful load. As the builder, I opted to placard my Eze to 1200 pounds. Doing the math, a Long-EZ, by the book, would have to weigh around 920 pounds empty to have the same useful load. Many Long-EZs out there are this heavy or heavier, and consequently are operated beyond the max gross weight prescribed by Rutan.
One thing to look at with either airplane is the empty weight, and the placarded max gross weight. I'm sure there are non-builder owners who operate beyond the weight that is physically placarded as the max weight for their airplane - doing this, and having a crack-up, and having a determination made that one was operating beyond the placarded weight can have some fun legal and insurance consequences.
Regardless of the type you may purchase, definitely have a qualified builder of the same type have a good look at your potential purchase. Also, if looking at a VariEze, make sure any help you have in assessing the condition of the airplane is done by an experienced VariEze builder - there are some differences in the VariEze (wing attach, for example) that a Long-EZ-only builder may not undertand well enough to give a sound evaluation.
I have flown 5 different Long-EZs, and two VariEzes over the past 22 years. Each one had some small level of uniqueness, based on fit, finish, engine type, etc. They all flew very well. I am partial to the VariEze because it suits my mission requirements. My far-better half enjoys local flights, and some cross-country work, and I made every effort to ensure the back seat fit her profile as well as possible. This is key. Having built my Ezes, I added one inch of width, primarily to give a little more shoulder room for the back-seater. I'm 6' and 210 pounds, and broad-shouldered. A "stock" VariEze's upper longerons made solid contact with my shoulders , in the back seat. One inch of extra width back there made significant difference. The Long-EZ is about 1.5 to 2 inches wider than a VariEze, inside, which is a big difference if you or your back seater are big people.
Hope this helps,
-Joe Person
VariEze N79JN
Bothell, WA (KPAE)
Good luck