Like Ewok, I have tried all 3 in closed beta with the lvl 31 template and also leveled a couple fo them to 10-12. The only one I tried to an extent was the Bright Wizard.
Bright Wizard
I agree with Ewok that the Bright Wizard feels to be the most powerful of the three. The AoE and DoTs are amazing. Most DoT's have a long range and the ones that are instant cast can be used on the move, making them helpful. I found all three mastery lines where pretty good and I felt like a "glass cannon".
The fire graphics for abilities are just amazing. Mythic did an outstanding job with that. I played the Bright Wizard in both a patch where they were gimped and one where they were buffed. Played right, they excelled both times. This class is exceptional in PvE, Open Wolrd RvR, and Scenarios. They also look really cool.
Witch Hunter
It is hard to talk about the Witch Hunter without comparing it to a WoW Rogue. They have stealth, positional attacks and a combo point system (accusations). The stealth is pretty weak in WAR and you will not be one shoting or chain stunning anyone. I played one to level 12 and discovered that you kill things in PvE really quick. Faster than a Bright Wizard.
In Scenario RvR and Open RvR, you really have to pick your targets and play smart. I topped damage in Scenarios on multiple occasions, along with kills and killing blows. Open RvR you have to be more careful to avoid the zerg. I got eaten alive by the zerg on multiple occassions on the 31 template before I changed strategies. More changes are coming to the Witch Hunter that I think will improve them. A fun class in PvE and RvR. They also look cool (it's gotta be the hats.)
Shadow Warrior
I once again agree with Ewok about this class. Choosing your stances at the right times makes a huge difference. If you can master moving and shooting, you will do exceptionally well. I had the least amount of experience with this one out of the three, but it felt solid to me when playing it. (Except for the elf part

).
Other Notes
I have had fun with almost every class that I have tried. The hardest for me was the Shaman, Maurader, and Archmage. Not sure why, the mechanics where good, just not my playstyle. Whichever class you choose really requires skill, which is what I liked. Also throw away any preconceptions about tanks that you ay have had in other MMO's. For the most part, Mythic got RvR & Tank to mix well.
I hope that answered some of your questions.