Umm, you mean E46 cars by that date (99-04) and the last year of the E36 (98), or did you mean 99-04 E46's?
They look the same basically with some differences in the lights (facelift vs pre-facelift, and the rear light designs). Other than that, not much changed.. Engine update in 2001 from 323/328 to 325/330, slightly more compression (hp gain) from the 323 to 325, and a bit more from the 2.8l to the 3.0l in the 328 and 330 respectively.
Course that's not even mentioning the M3, king of the 3 series.
The best? Hmm.. I like the M Coupe (unique M hatchback, only made for 3 years) and the M3 (cabrio!). Then any BMW cabrio, I don't care what engine..
After that, any sedan (BMW sedans just look so good..). Coupe last (sorry I'm old), looks great, but I have my preferences!
As for hiccups? There were some issues with 2001's having touchy steering issues, and the latest steptronic problems in mid-late 2003. I'm not aware of any others, but plenty of folks share their fortunes (and misfortunes) here with their cars.