Just because I possibly could, I tried networking the old and new machines via the two sockets on the router.
Vista recognised Win7 right away, and after some fiddling with permissions I found out how to add folders. Win7 however... it turned out the firewall I had on Vista was blocking access. There were passwords involved in this, but just like on TV shows guessing only took a few seconds.
Win7 has a new networking for dummies system called Homegroups, but that only recognises other Win7 machines.