How does it run poorly on Tiger? In my experience Tiger has always, 100% of time been very noticeably faster than Panther. Tiger is literally an optimized version of Panther with a few added features that have relatively low overhead. Much like Snow Leopard to Leopard. There is basically no reason to run Panther other than novelty. Tiger is better, and faster even on slow G3s. This is not opinion, it is fact. I even have Tiger on Beige G3s.
A lot of users on here disable dashboard on Tiger. I never do. It doesn't do anything IMO and I use it even on very slow G3s. What I do disable, is spotlight indexing. If Spotlight is indexing it slows even mid-range G4s to a halt IMO.
Your G3 will never be good at web browsing. I have the same iBook (amongst many other G3s).
How much ram does your system have? The HDD could also be going out. Max the ram out if it isn't, a slap in an SSD and your iBook should be a decent Tiger machine as far as G3s go.