Just replaced my Apple Time Capsule with a newer one. Here's what I found to be the best approach in moving data and time-machine backups to the new unit.
Hook-up your Mac to an ethernet-port of the old time-capsule. You can use Network Utility or ifconfig to verify gigabit connectivity. This is something you do not want to do over the wireless network.
Second step is connecting a switch-port of the old time-capsule to a switch-port of the new unit. You can use both a straight or crossed networkcable.
Disable time-machine on your Mac (Time Machine in System Preferences) and make use no machine in the network is using the disk of the old unit.
Mount both time-capsules on you Mac from Finder. Just click the volumes on both units. Browse to the root of the data-volume on the old unit. Select and drag the time-machine images from the old unit to the new unit.
You can copy the remaining data to the new unit in one or multiple batches.
Next step is optional. It's resizing the Time Machine sparse-bundle (eg., backup disk-image). If you upgrade from, let's say, a 1TB Time Capsule to a 2TB unit you Time Machine sparse-bundle is max. 1TB in size. If you expect a large Time Machine backup you can use this command from Terminal.app to resize the sparse-bundle.