Tiger ran a lot faster on my G4 Powerbook.
Since it has a larger memory footprint than Panther, though, 512MB is going to slow it down to below Panther speeds - I had 1.25 GB in the machine I upgraded from Panther to Tiger.
I didn't notice any difference in *stability* - neither system ever crashed on me (apart from once, IIRC, when I connected/disconnected an audio interface but hadn't installed the driver yet).