Be you a Druid player, you may know that Druids are limited to being Night Elves if they play as the Alliance and Tauren if they are with the Horde. Generally speaking, WoW developers have stated that their design philosophy is to make race choice be relatively insignificant, so that players of any particular class do not feel compelled to make that class a certain race. You're going to be spending a great deal of time with this character, so your first priority should be picking a race that appeals to you if you've always wanted to play an elf, for instance, don't create a Tauren just because you've heard their abilities are a little better for druids, or vice versa.
Between the Tauren and Night Elf Druid, there are many differences in regard to both racial abilities and aesthetics for the most part.
For one thing, Shadowmeld is situational but can be very useful. It is convenient as it lets you stealth out of sight of players and wandering monsters, allowing you to go AFK for a few moments if necessary- although once you get cat-form you will be able to do this anyway. Tactically, the stealth won't be cancelled until a spell is actually cast, rather than while it is being channeled, so if you are able to get in range of an enemy you can shadowmeld and charge up a damage spell such as starfire in order to catch your enemy completely by surprise. Definitely most useful for balance druids (who focus on damaging magic spells). Shadowmeld also increases the effectiveness of your stealth ability slightly, making you slightly harder to locate when you're stealthed. However, it is useful, in particular on a PVP server.
For another, Teleport Moonglade to some extent is able to teleport the caster to the Druid village of Nighthaven in Moonglade. Both Tauren and Night Elf druids get this spell, which teleports them at level 10 to a small village controlled by the neutral Cenarion Circle druidic organization. This can be used as an alternate means of getting around the world, as druids can teleport from anywhere in the world to Moonglade. For Night Elves, this spell is very convenient, as it is a short 2 minute or so flight from there to the Night Elf capital of Darnassus, which is otherwise a 15-20 minute trip from the other alliance capitals in the Eastern Kingdoms. The spell has somewhat less of a utility for Tauren druids, as after going there only option until they get to max level is 10 minute flight to Thunderbluff. Basically, for Night Elves the spell almost acts as a second hearthstone to get back to a capital city in a hurry, whereas for Tauren.
For Tauren, War Stomp is a very useful ability, although not useable by a druid in any form save Caster and Moonkin. This provides Druids an extra spell interrupt, as well as the ability to buy some time to get off a heal while they are being attacked at close range.
Endurance provides a small amount of extra health. More health is always useful, and this ability has a slight bit more utility than the Night Elves' extra dodge. Dodge may help you avoid a melee hit or two, but having extra health lets you live longer from any type of attack, not just melee.
If you are a herbalist, Cultivation is somewhat useful. Any herbalist will eventually be able to pick every herb in the game, however, regardless of race, so in the long run this skill will not matter much.
Some Druid forms look different depending on whether you choose a Night Elf or Tauren. For some people, these differences may be enough to prompt them to choose one race over another.
In cat-form, Tauren Druids look somewhat like lions with horns sticking out of their heads, while Night Elf Druids look like Puma's or Panthers. In bear-form, Tauren Druids have bull horns coming out of their bear's head while Night Elf Druids have swept back, even ears on their bear.