Gmail on mobile still doesn't have a unified inbox, and it also doesn't have features I've come to depend on such as snoozing messages. I usually use Inbox by Gmail on mobile, which also lacks a unified inbox and (bizarrely enough) support for HTML signatures but does have pretty good message snoozing, and I like how it handles bundling.
Outlook (incidentally, another example of my original complaint, as it's just former email startup Acompli with a fresh skin although obviously it's probably not getting shut down anytime too soon) doesn't have very good message searching for Gmail, which is a common complaint I have for non-Google mail apps. Obviously, I get that Google has a huge built-in advantage here; but if your email app is going to support the "Mailbox paradigm" of abandoning folders/traditional labels in favor of just marking things as done, it also needs to have search functionality that can back it up. Outlook was also really buggy for me when I last tried it, although that was a little while ago so it may have improved.
The new Outlook app is actually surprisingly good. I think the Sunrise guys (sunrise.am) are running that team and it shows. I laughed the first 2 times friends recommended me the app, but I tried it and now also highly recommend it.
My favorite tiny detail is that I can tune the notifications to push only unread counts to the icon badge and only for the "focused" inbox. That means I can avoid constant push notices for email yet still be able to glance down when I want to and see if I have any unread emails that are actual human communications.
Message searching for Gmail in Outlook iOS/Android is piped directly from Gmail itself. Your search is forwarded on to them and results are displayed back in the app. Immediate search results are from on-device and then filled with the Gmail results after they are received. So if the results are bad, then maybe Gmail has a secret API they use to make their app better.
Outlook (incidentally, another example of my original complaint, as it's just former email startup Acompli with a fresh skin although obviously it's probably not getting shut down anytime too soon) doesn't have very good message searching for Gmail, which is a common complaint I have for non-Google mail apps. Obviously, I get that Google has a huge built-in advantage here; but if your email app is going to support the "Mailbox paradigm" of abandoning folders/traditional labels in favor of just marking things as done, it also needs to have search functionality that can back it up. Outlook was also really buggy for me when I last tried it, although that was a little while ago so it may have improved.