Ok, not going to proclaim myself an expert, but I've leveled both to 40+ and can make some assumptions from that.
Assassin: Very powerful attacks, top of the two for raw dps.
Brigand: Very good attacks, top of the two for soloing
I liked my assassin when playing with a bruiser friend, because when it hit the fan if he could hold agro I could put some major pain on mobs. I had 5 or more nasty backstab style attacks, they hit hard, and with the ability to lend him a portion of my agro he held them fine.
Downside, when by myself (the solo Kunark boat mission before RoK comes to mind) with more than one mob I was in trouble, very hard to get in those backstabs when said mobs are beating you down. Positional requirements make assassin harder to solo with (but not impossible) than other classes.
Once I decided to try the brigand, I fell in love with the class. I shot to lvl 25 in 2 days of play. If I wasn't matching my lvls with friends I could be at least lvl 70 now. The brigand has so many stuns he can lock down mobs to allow for his back facing attacks, and the attacks themselves hit pretty dang hard. While multiple mobs are harder than what I've seen other classes deal with, much better than the assassin.
Not to say that soloing is his only value, he is great in groups. I can offtank mobs that are eating the healer face until the tank gets them back, my stuns and debuffs keep the main target locked down and drop him easier. I don't do as much dps as my assassin, but I feel like I have a lot more flexibility. Plus I get some very group friendly abilities like Smuggle (group stealth), which has aided in doing heritage quest lines in Qeynos.
I'll add some more details later, but I would say either class is great to play, just with different foci. If you are thinking about giving EQ2 a try, you can't go wrong embracing the shadows with either.
If you want to play solo, roll a shadowknight. best solo class, bar none. I could've soloed 1-80 i think, though t6 and t7 would've been slow.
If you want to stick with your friends and still are looking to play the stealther, I recommend swashbuckler. I played on a PVP server so swashbuckler wasn't an option, but they are probably my favorite class. After that, I'd say brigand. Assassins are so boring. Ooo more damage... swash dps > assassin dps.