I used to have a similar eMac, the 1GHz ATI, which came with 10.2. I upgraded it to 10.3 which was a great OS. This eMac only had 256Kb of RAM as standard. When I added another 512Kb it speeded it up considerably as it did not have to swap data out to the HD as frequently. The performance improvement was quite noticeable. Later I added a second 512Kb to max it out at 1GB of RAM, but as an example of diminishing returns, it did not improve things much.
I did not run Tiger on it, but did install 10.5 and found that taxed the resources too heavily making it too slow and so went back to 10.3.
Before you give up on 10.4, which I imagined the 1GHz ATI would run well on, have you maxed out the RAM to 1GHz, and allowed for sufficient free space on the small hard drive, say keeping about 10GB free?