DOW is a fraggin' awesome game!
It's not as balanced as StarCraft, but then what is?! That game is a work of art!
That said, it's balance is okay - If you LEARN your side, you can beat almost any other side, but you have to be very flexible.
It also depends heavily on what your objectives are and the map size.
On a small map with annihilate, a good marine player can destroy almost anyone.
On a large annihilate map, eldar are very hard to defeat - They can drop fire-prisms in the middle of your base which has pretty much the same effect as the 9xPrism-tank|Chronosphere finisher in C&C.
We normally play take-and-hold type mission: All sides are very balanced in that.
Orks and Eldar are very good at taking points, but have trouble holding them whereas both Marine-types are harder to capture points with but once they dig in they're bloody hard to get rid of without using all your forces.
Eldar are my favorite team - They the fastest race in the game and you can capture lots of points very early on. Their agility also lets them wizz from one side of the map to the other, which is awesome for counter-attacks and reinforcing.
The other race I tend to play are the Space Marines - They play very differently than the Eldar - Unlike the Eldar, their units are built like brick s**t-houses, but they are very slow, so you have to plan well in advance because it's hard to reinforce them if something goes wrong. The one trick they have up their sleave is their teleport beacon - Dropping a commander unit into a scouted base so he can nuke it, or just a crap-load of dreadnoughts anywhere, is great fun

I don't have too much experience with Chaos or Orks, but I do know the Squiggoth is a right bastard to get rid of

The Avatar and Khorne suck compared to the Squiggoth - You can kill them with some upgraded commander units and some dreads/fire-prisms! The squiggy on the other hand... haven't found a good way to counter it aside from throwing lots of bodies at it until it goes away
