Gmail or Outlook as a replacement webmail provider?

[#1]

Spent a very long and frustrating day yesterday trying to recover the situation having discovered that the Inbox of one of my two Plusnet email accounts was suddenly empty except for a single new message (it should have had a few hundred in it.)
Client is Thunderbird, both accounts are IMAP, and it's hard to think of anything I did which could have caused it to happen.
I had taken a 'Mozbackup' in February which seemed to be the best way to at least partly recover the situation, but all that happened after restore was that both accounts were duplicated, and none of my emails were restored to any of them. I also noticed that the IMAP accounts had somehow both reverted to POP3 accounts! 
Think it's time to move to a more modern webmail system  - Gmail and Outlook look to be the front-runners, but I'm a bit disturbed by comments I've read about how the Jan 2016 revisions to Outlook have more or less wrecked it for some users.
Email never used to be this flaky - I'd be very interested to hear anyone's views about the webmail system they use, particularly the above two.

[#2]

Don't like to see unanswered emails on forums, especially a) now the new forum software gives you a daily reminder of them, and b) when it was me who started this particular specimen , so thought I'd update it with my experiences with Outlook online and Gmail.

Thunderbird/Outlook repeatedly failed to upload and sync my existing folders, sometimes getting about half way through the contents of each before just giving up - very frustrating.

No such problems with Gmail, although I'd still prefer folders rather than 'labels', and unless you use the Chrome browser you don't get notifications of new email arrivals, although you can still use Thunderbird as a client for Gmail if you enable 'use less secure apps' in Gmail.

Will keep my PN IMAP addresses for a bit longer to make sure Gmail doesn't display any strange habits I could do without...