In other webapps I've done I've always sent email from the same domain as the app. However for my next project I'm thinking of using a related domain. For example if my webapp domain was widgets.com the report emails would originate from widgets-reports.com
The app sends daily reports and I'm wary of getting blacklisted as a spammer. The emails are opt-in but in the past I've encountered users flagging automatic email they request as spam instead of disabling emails.
If I send from a related domain I should be able move to a new IP if necessary without disrupting the service's primary email. I really can't think of a downside other than user's expectations that mails would originate from the app domain.