As long as both TC are bridged or one bridged and one router then it will work fine.. you cannot use ethernet if the TC is set to wireless extend.
Plug the old TC LAN port into the new TC LAN port..
Old TC in bridge mode.
Instructions for moving sparsebundles are here.
Transfer TM backups..
Apple doco. http://support.apple.com/kb/ht5097
Pondini doco http://pondini.org/TM/18.html
IMHO it is much better to archive the old ones.. and start TM afresh on the new TC.. but that is purely personal.