I'm stealing screenshots from Kinless and Potshot to demonstrate the difference between the graphics of World of Warcraft and Lord of the Rings Online. I could have done screenshots myself, but I thought using what other people think are typical screenshots of the game they are playing would be better.
The difference in style is very visible. WoW uses a lot more color, and is more comic style. LotRO's colors are more subdued and natural, without falling into the grey-in-brown trap like EQ2 did. LotRO has a significantly higher polygon count, and looks more realistic, just compare the trees. The over two years difference in age is noticeable, although of course that comes with the downside of probably needing a 2-year younger PC. In WoW your "shadow" is a round spot, regardless of your size or shape. In LotRO your shadow looks like it should look, a 2D image of you on the ground. I was seriously impressed when I crossed a ford in LotRO and noticed that in the water I could see both my shadow and my reflection. Water looks *so* much better in LotRO.
I always liked the WoW comic style. It has the advantage that you can exaggerate proportions to make things more visible. For example the treasure chests in WoW really shout "treasure" at you. LotRO's clickable items are smaller and less visible, but the game gets around that problem by adding an optional floating title to everything you can click on, and having important clickable things pulsate. I didn't like the photorealistic graphics of EQ2 or Vanguard very much. But I do like LotRO's graphics better than WoW's, although I must say WoW has the better animations. For me it is easier to imagine that I am living in another world if that world looks more natural.
Another important difference is how the characters look. I mentioned before that I made a female blood-elf, because I couldn't manage to create a male blood-elf character that didn't look too much like a pretty boy. If I would create several male blood elves, they would all look like pretty boys, just with different hair styles. In LotRO I managed to make two totally different looking hobbits, one old and gray, with a pot-belly, and the other young, with freckles, and muscular. Especially for a role-playing server it is important that you can deviate from the standard good-looking adventurer stereotype. In WoW, if you want to play somebody ugly, you need to choose a Horde race. In LotRO you can change the body type, or add wrinkles or scars to your face.
Both graphics styles are certainly viable, and if you have an elderly computer you might prefer the lesser system requirements of World of Warcraft. But if your computer is half-decent, Lord of the Rings Online sure is pretty. I'm a big fan of Nagrand, but The Shire beats it hands-down. I've always been an explorer, and having a beautiful world with impressive graphics makes that so much more pleasant.