Hi Esperahol,
Most water filters do not get rid of the chlorine very well. I believe they are better at removing heavy metal than removing chlorine and chlormaine. I don't know for sure how every one of them work, but once some of the aquarium hobbyists had done some tests with multiple water filters. The best one was only able to remove about 40% of the chlorine from the tap water. I don't remember the exact brand/model they were testing, so what I just said is inconclusive.
Yes, birds are much more fragile creatures than dogs and cats. Better safe than sorry, I recommend using purified water, bottled water, or boiled (then cooled) tap water for the birds to drink and bath.
