Actually, you don't even need that vine server on your Leopard machine, or on your Tiger machine (I'm a little unclear who is who on your working configuration and who is who on your not-working configuration).
If you want to use your Tiger machine (VNC client) to access the Leopard machine (VNC server), then on the Leopard machine, go to Sys Prefs > Sharing, check the Screen Sharing checkbox, and click on the "Computer settings..." button. In the resulting popup, check the "VNC viewers may control screen with password" checkbox and enter the password that you will require the Tiger client to use to connect with their VNC client program. I assume you are using CotVNC or JollysFastVNC as the VNC client program on your Tiger machine?
Now, if I got the direction backwards, here is what you would do to use your Leopard machine (VNC client) to access the Tiger machine (VNC server): On the Tiger machine, go to Sys Prefs > Sharing and check the Apple Remote Desktop checkbox on the Services panel. I think that would do it.
Now, I, personally, further configure my Tiger machine to allow VNC from other Tigers as well as from Leopard's Screen Sharing program in Leopard, so while I don't think you would have to do the following for Leopard-only clients, if the above isn't working, then try these additional steps:
First, click on the Tiger (VNC server) Firewall tab in Sys Prefs Sharing. Click "New." There is a pulldown menu in the resulting popup where you can choose "VNC." Choose it. It will "quickfill" the port entry information for you. Save those changes and exit.
If that still doesn't do it, then return to Sys Prefs > Sharing > Services panel. With the Apple Remote Desktop service checkboxed and highlighted/selected, click on the "Access Privileges" In the top part of the resulting popup, you can grant access privileges by user; fill out as desired. In the bottom part, check the "VNC viewers may control screen with password" checkbox. IF you were allowing VNC access from other Tigers, use the password that you would want VNC clients to use. I think you probably need something in there if you have to do this last step.
By the way, you know that, in Leopard, you can launch Screen sharing from Finder by doing a ⌘k and typing in "vnc://{name of remote computer goes here}", right? Also, if you haven't already done so, you may find it convenient to drag /System/Library/CoreServices/Screen Sharing.app onto your dock and/or make an alias of it in your Applications folder.
