Most likely your app site is not being indexed, given it probably requires authentication, thus you probably don't have to worry about SEO value. Other sites that are not your primary marketing site (for example your support knowledge base or things like that) may benefit from being on the same primary domain. There may even be an argument for putting it on a subdomain, however this does make integrating with external services more difficult (although it can be done).
If you are running an operationally important service, then there is actually at least one thing you should have on a separate domain: your status site. That way if something goes terribly wrong with your primary domain you can at least access your status site to report the issue to customers.
One thing that can be either a benefit or a drawback, depending on how you use it, is the fact that subdomains have easy access to cookies, whereas I am not sure that is the case across different domains. It can be an advantage for connecting visits across sites together, but it can be a disadvantage if important cookie data leaks from your application over to non-application sites. Example article that talks about it (there are more): http://erik.io/blog/2014/03/04/definitive-guide-to-cookie-domains/
(For us at DNSimple we just use subdomains except when we want a unique marketable domain, like https://howdns.works or other micro-sites, and for our status site.)