I've had a Google Apps for Business account for years, for myself and members of my family, even though I primarily work for an organization.
In a world where every person is really their own corporation (whether actually or just practically), and you're managing the marketing and selling of yourself and the delivery of your services to other entities (aka employers), having a personal/corporate e-mail makes sense!
I'm extremely happy with the GMail interface and Google's service and reliability. I use lots of extensions like ActiveInbox for which I have a lifetime account (or April 8, 2103, whichever comes first). My whole workflow is dependent upon GMail and Google Apps. $50 per year per user to Sergey and Larry is perfectly reasonable.
The trouble is, there are limitations to creating a unified inbox within the GMail interface.
For years now I've had the work e-mail address I use with my main client (or as it is quaintly referred to, my "employer") simply redirect into my GMail account. I can then have a unified inbox and "send as" from that work e-mail address.
But finally my workplace decided to get beyond a simple e-mail server system and adopt Microsoft 365. No complaints. Good move. (365 is the Microsoft hosted version of their 20 year-old Exchange back-end system for e-mail, calendar and contacts.)
The challenge is that 365 and GMail don't play nice together. You can not call 365 e-mail into GMail with IMAP. (Internet Message Access Protocol is an Application Layer Internet protocol that allows an e-mail client to access and synchronize with e-mail on a remote mail server, such as 365.) This limitation has nothing to do with Microsoft. Google doesn't allow you to make any IMAP calls from GMail. It only allows you to use POP to access an external account, and that's slow and frustrating. E-mail will only be checked every 5 minutes, at best. It won't be nicely synchronized. Google uses an algorithm that determines how often you're using an external account and decides how often you need it checked. There's no way of setting this cycle manually. And I've never seen it less than every 5 minutes.
Going the other direction, you can not use the "connected accounts" feature to pull your GMail into 365. Try it. You won't have success. Other e-mail systems, such as Outlook or Postbox, can IMAP with GMail just fine. But pulling it directly into 365 itself won't work. Microsoft and Google maintain mutual incompatibility and point fingers at each other (although, I think there's evidence that it's Microsoft not Google that's trying to play nice). But even if this did work, I would lose my beloved GMail interface.
I could have a copy of all my 365 mail forwarded into GMail and then continue to "reply as" from within GMail. But my employer (since we're talking Microsoft, we'll use that old fashioned term) will be appropriately annoyed at me if I do that because they want custody over the e-mail. Same goes for POP, even if I accept the limitations noted above of that system with GMail. Again, no complaints. That's correct from the employer POV.
The only solution I've found is to run two browser windows, one with my work e-mail and one with my beloved GMail interface. Sadly, no unified inbox. I've got nothing against the 365 browser interface. The 365 interface is extremely good if you're comfortable with the 20th century notion of a database that Microsoft still maintains, where every e-mail is an object and can only be in one place at a time. There's probably some third party solution for a single browser interface that produces a unified inbox. Yahoo Mail perhaps? But again, I have no interest in even trying because I'm hooked on the world of GMail where folders are just representations of search results based on tagging and e-mails can be in an infinite number of places at the same time. Perhaps Google simply can't figure out how to create a unified inbox in which calls to a remove server are being made via IMAP. Whether it's a limitation of the GMail architecture or a Google strategy, I won't hold my breath for this feature.
At least on the mobile side, there are solutions. BlackBerry has this unified inbox thing down. Far and away the best mobile device for managing multiple inboxes is a BlackBerry Playbook or a BlackBerry 10 device. Set-up with an Exchange account couldn't be simpler. You've then got a unified inbox with all your e-mails co-mingled and your Twitter and Facebook messages co-mingled too. Apple also plays nice, with a unified inbox on IOS. But again, this isn't the GMail interface I've come to depend on. Android? Same problem as browser-based GMail. You have to run both GMail and a separate Android e-mail app.
The other problem is calendaring and contacts but for that there is a solution. You can't directly synchronize calendars and contacts between Microsoft 365 and Google. For calendaring and contacts, use a program called OggSync. I've been using it for a few days now. It appears to be flawless. Running Outlook 2013 with OggSync creates an almost instantaneous bi-directional conduit between Google calendar and contacts and their counterparts in 365. Of course, you have to periodically open up Outlook on your desktop. And I don't know of a Mac equivalent.
Interestingly, if my employer had switched to Google Apps instead of 365, I'm pretty sure it would not have worked as well as Google with 365. I would have been faced with the same problem with e-mail, needing to work from two separate browser windows, and I'm not sure if I could have produced a sync between the two accounts for calendars or contacts.