Sorry, I didn't notice that the other model you had was the same as the one you asked about. Flashing this one with the same BIOS version as the other has could help, but if the other one has an older BIOS I don't know if you'll be able to, sometimes you can't install older versions than what you have.
It could also be that 512MB sticks are all that's officially supported, and you just got lucky with the other Vaio, like maybe it has some seemingly minor internal difference that allows it to support 1GB sticks. I don't think there would be anything special about the 1GB sticks you have in the other Vaio, but maybe you could try them in this one too.