I'm curious because we'll have to migrate to a better email provider in a month or two, and Gmail enterprise seemed to be the best fit for us (price, storage, good iOS app to leverage push notifications, etc).
On push, Google Apps gives you ActiveSync as a protocol, as an alternative to IMAP. But the integration with iOS Mail is weird and I could not use it.
But FastMail on the other hand, in a twisted turn of events supports push through Apple's own APN, getting the same treatment as iCloud: https://blog.fastmail.com/2015/07/17/push-email-now-availabl...
FastMail also has a native app that does push notifications, but it's just the packaged web interacts with push notifications added. This is both good and bad. It's good because the mobile web interface is very decent, compared to Gmail, and this means you always have a decent UI on whatever OS you have. It's bad because it doesn't feel native, but then there's nothing more native than the iOS Mail app.
I've been a Fastmail user for almost 10 years. Never an issue that was not solved in very short order and most professionally. Fastmail offer a modern product with old world service and charm. A win-win.