While this is a difficult question to answer definitively without knowing a person’s specific requirements, the answer in a vast majority of cases will be an unqualified “No.”
iCloud Mail is designed to be a very simple, basic e-mail service that’s reasonably adequate for the average personal, home user. Somebody who typically uses their ISP’s e-mail service would probably be a good candidate for moving to iCloud Mail, as it will likely offer more features and a more portable e-mail address.
However, iCloud Mail will lack many of the features that Gmail users have likely become accustomed to, such as:
Flexible e-mail addresses. With iCloud you must use an iCloud address (generally @iCloud.com) for everything. There are no provisions for using alternate e-mail addresses in the web UI at all (MobileMe introduced this in mid-2010, but it was removed when iCloud was rolled out). If you use an external e-mail client such as Apple Mail, Outlook Thunderbird, etc., you can work around this, but it’s kludgy and generally more complicated than it’s worth. On iOS this can be even more complicated. The bottom line is that unless you’re happy using your iCloud address for everything going forward, it’s not worth the switch. You can specify up to three aliases with iCloud mail, but they must all be @icloud.com addresses (users who had iCloud accounts before late 2012 can also still use their @me.com addresses, and users who have had accounts before 2008 can still use their @mac.com address
Spam Filtering. Gmail’s spam filtering is excellent. iCloud’s is one of the worst I’ve seen – better than what an ISP will likely provide, worse than any other mainstream webmail service out there. Desktop mail clients can make up for some of this (even Apple Mail has better spam filtering than iCloud) if you’re willing to leave your computer on with your Mail client running all the time.
Rules/Filters. iCloud does have a few server-side rules, but they’re basically limited in flexibility to move-to-folder, delete, and auto-forward rules, as well as a pre-defined vacation responder which is basically an inflexible “reply-to-all-messages” rule. Conditions are also limited to From/To/Subject. Again, desktop mail clients have more options, but these must be running, and are not iCloud-specific anyway — you can use Apple Mail and Outlook with Gmail as well via IMAP, of course.
Push e-mail. iCloud does provide push notifications for e-mail on your iOS devices, after a fashion. You get notified of NEW messages, but the notification badge won’t clear if you read those messages on another device, or move them into folders. Gmail, if setup using Google Sync,
will provide full push-based reconciliation of Mail, and even provides the ability to push additional folders beyond just the Inbox, so you always have your current mail available for offline use (note: Google Sync was discontinued for free Gmail users in Dec. 2012, although it remains available for paying G Suite users). Google also provides its own native Gmail iOS app that takes advantage of push notifications, and again offers full reconciliation.
Search. Gmail obviously excels in search, and finding stuff in Gmail is fast and convenient. iCloud Mail does provide search capabilities, but they’re slower and work on a folder-by-folder basis in the webmail client. Apple Mail, via Spotlight as does Outlook on Windows, but like rules and filters those are functions of the apps themselves and can be used with any e-mail service.
Storage. While iCloud gives you 5GB free, that’s not just for mail; the 5GB is shared with almost everything else you store in iCloud, including iOS device backups and data from iCloud-enabled apps, although Photo Stream and iTunes content do not count against your 5GB quota.
Conversation Threading. Not everybody is a fan of this feature, but Gmail’s conversation threading is far better than most other mail services and clients. The big advantage here is that Gmail provides threading globally across the entire mailbox, while iCloud Mail is limited to threading only those messages that are in the current folder.
There are a host of other advantages of Gmail over iCloud as well, such as two-factor authentication for increased security, more innovation in terms of new features, and support for third-party web apps such as Rapportive and Boomerang.
Obviously if you’re already using a third-party client rather than the Gmail web interface, some of these differences are less of an issue as you’re really using Gmail as just-another-mail-server in that case. However, even here things like spam filtering and the inflexibility of multiple from addresses will still be of some concern.
I should also add that there’s no reason that you can’t use some features of iCloud, such as Calendar and Contact sync, while still continuing to use Gmail for your e-mail. Any Apple ID can be used for iCloud — you only need an @icloud.com Apple ID for the e-mail service.
Updated 2017–09–28 to change references to @me.com addresses (pre-2013) to @iCloud.com addresses, update references to Google Sync being discontinued for free accounts, and adding mention of Google’s native Gmail app for iOS devices. Removed reference to Apple Mail apps threading conversations only in current folders, as this capability was added in iOS 10 and macOS Yosemite.