iTunes sync podcasts
You can copy the list of subscriptions between them, but I don’t know how to keep them in sync.


In the sidebar of the first iTunes installation, select Podcasts, right click, then click Export. I use the OPML file type, but others might work. (Let’s call it Podcasts.opml).
Using a USB stick, Dropbox, or some other method, transfer Podcasts.opml to the computer with the second iTunes installation.
Select File > Add to Library, and find Podcasts.opml. Once you open it, your second iTunes installation will have the same podcast subscriptions as the first.


Two comments:


This won’t keep them in sync; if your podcast subscriptions change, you’ll need to repeat the above to carry the changes across.
There may well be a much easier method, using something like Home Sharing or Dropbox, to keep the single library file synced between the two machines.