Biggest difference between Gmail and FastMail in how they handle email is tags vs classic IMAP folders. This can be a turn off for people, but for my personal email I discovered that I want folders. This is because my personal email also has the role of backing up my work email. I've lost work email in the past when switching jobs and I don't want that to happen again. And with FastMail I can simply download my work email in its own folder, so it doesn't have to pollute my personal email. FastMail is also very flexible in its settings. Setting up filters is easy in Gmail but limited compared with what you can do with those Sieve scripts in FastMail. Speaking of the interface, I now like FastMail's interface more, as it makes it easier to switch between folders, or back and forth between email, calendar, contacts or notes.
SPAM filtering in Gmail is said to be extremely good, however a certain class of spam has been reaching my Gmail Inbox for the past 2 years with me being unable to stop it - I made the mistake of giving away an email address on my blog and now I get emails related to SEO marketing and bullshit. In Gmail I cannot setup a filter that automatically marks an email as spam if it contains the word SEO. But in FastMail I can do just that.
FastMail does CalDAV for the calendar and CardDAV for their contacts. I can sync my Android phone and it works out great. IMAP is also very responsive and standards compliant. And personally I feel good about rewarding a smaller player that plays nice with others because monoculture are bad ;-)
Another thing I did after that was to create 2 Google accounts. I'm using one Google account for Google Play purchases and nothing else. This is because Google Play purchases are not transferable. So for example I have an old phone lying around that I gave to my son for playing. Restricted accounts only work on tablets, don't know why, so my son ended up having access to my email, which is not cool. Plus I'm all for paying for apps, but I should be able to share my purchases with my wife. Like if I buy a GPS device, we can both use it, but if I buy a maps app my wife can't borrow it without borrowing my account, along with my email. And I don't like this kind of lock-in.
There are some downsides. I could not find a good email client that can do IMAP Idle. FastMail's app works on Android but I don't like the UI. On the bright side that app is simply exposing their web interface, so FastMail works very well in a mobile browser, something that Gmail doesn't do and it matters when borrowing other people's devices.
All in all it's been a great transition for me and best of all is that I can now try out other Google services and products without feeling remorse or fear of lock-in ;-)
CalDav is also shoddily implemented; for example, on android using fastmail's recommended 3rd party caldav sync, creating a meeting on your phone (calendar client using caldav to sync to fastmail calendar) will not send meeting invites. Surprise!
FastMail's message compose is also unusable on mobile firefox if there is quoted text in the compose area.
I use it because I'm removing google products from my life; you should just watch for the above bugs.
You are right that FastMail doesn't send out invitations when using third-party clients. FastMail is mentioning it on their page [1] promising they'll implement it, however I think this should not be the job of FastMail, but that of the client. For example this works fine in Thunderbird because Thunderbird sends those invites by itself, all you need to do is to specify which email address is linked to which calendar. Thunderbird sends invitations by itself for regular CalDAV accounts, but with a Google Calendar it doesn't do that because it is Google's Calendar that it is special. In this case it is the CalDAV-Sync integration that should send the invite.
Mobile Firefox is new and it doesn't surprise me that FastMail's compose doesn't work in it, because it has weird behavior when I interact with text boxes. I also use Firefox on my Android, but not for mobile web apps. It's currently too unpolished for that. But I'm sure that some bug reports will help.
One thing I'm happy about with FastMail is that things improve. For example they weren't supporting CardDAV for family accounts before August. Now they do and I'm pleased with it, though I wouldn't mind some extra functionality.
But that's the thing we are missing in the consumer / producer relationship, the direct relationship between the parties involved, the feedback. With Google there's nobody I can talk to, because they are too big to listen to individuals like myself. Usage of Google, Apple or Microsoft products leads to much like what happens in agriculture ... the rise of monocultures, the end of diversity and ultimately we end up with disastrous consequences for our own health.
How do your employers feel about that? If I tried that with my current employer, I'd be switching jobs straight away.
1: https://f-droid.org/repository/browse/?fdfilter=K9&fdid=com....
What this means is that in addition to trusting Gmail or FastMail with your data, you now have to trust a third-party as well. And that may be cool for others, but doesn't work for me.
On the plus side, it's open source and seems nice inside, so it shouldn't be hard to add support for regular old IMAP or JMAP if one wants.