Sluggish file transfer to Apple Time Capsule but only from one of my computers!

Hold down the option key on your Mac while you click on the Time Machine "clock" icon at the top of the Mac's screen.

Select and run Verify Backups

The process might take anywhere from 10-60 minutes or more depending on how much data is currently stored in the backup.

Post back on your results

On the G5......

Click on the Time Machine "clock" icon at the top of the screen

Click on Open Time Machine Preferences

Right-Click on the name of Backup Disk

Click on Stop Using the disk for Backup and confirm if asked

Restart the G5

Click on the Time Machine "clock" icon at the top of the screen

Click on Open Time Machine Preferences

Click on Add or Remove Disk

Select the name of the backup disk and click Use Disk

Check to see if a backup will run

If it does, go back to the previous set of instructions to Verify Disk to see if the operation will be able to correct current disk errors, which is causing the slow backups.

I'm surmising then, that the issue has to do with how the older OS handles available space on the disk... ?

Things will be equally slow with newer operating systems when the backup disk is close to full and Time Machine is trying to delete enough older files to make room for newer files.

On newer operating systems, there is no way to delete older files manually using the Time Machine interface like there is in Snow Leopard, so you will have to plan accordingly when other backups are close to being full. Sometimes, Time Machine cannot delete enough older files to make room for a newer backup and then you are stuck.