Which Should I Use: Subscriptions or Notify?

Both the subscriptions and notify modules have the same purpose, to let you know when new content has been added to the site.

Subscriptions require a little more work on your part but allows you to be specific in selecting what new content you want to be notified about.  Subscriptions has to be set on a per item basis.  Notify sends out a message whenever any new content has been added and requires little effort on your part, just turn it on in your profile.

Subscriptions sends out notification immediately after content has been added.  Notify can take up to six hours (based on site settings) to generate a message, Notify runs four times daily.

Subscriptions sends out one new message for each new content item.  Notify sends out one message containing links to all new content since its last message.

Which method you use is entirely up to you.  If you want instant notification of new content and don't mind the extra work turning on and off subscriptions then Subscriptions is your choice.  If you don't need to know if new content has been added immediately then Notify works very well.