When comparing Notion vs Apple Notes, the Slant community recommends Notion for most people. In the question“What is the best cross-platform note-taking app?” Notion is ranked 7th while Apple Notes is ranked 26th. The most important reason people chose Notion is:
Even the right-click menus on the web are the same as the app.
Specs
Ranked in these QuestionsQuestion Ranking
Pros
Pro Full-featured on desktop, mobile and web
Even the right-click menus on the web are the same as the app.
Pro Unlike anything else
One of the most complete applications one can use to build a personal dashboard (or professional) and migrate all other services to it. No more calendar, task, notes, financials, lists, writing and wiki apps, just Notion.
Pro Pages within pages within pages, to infinity
You can have a ridiculous amount of information within a single note. Look at how it works, you'll be surprised!
Pro Flexible contents storage and organization
You can upload files and embed online stuff in any hierarchical structure using pages, toggle lists, etc.
Pro Highly visual, with icons next to every new page and so on
This feature makes it very easy to find certain notes and such. And great for visual people as well. You could also add images as icons instead, if you like.
Pro Blocks offer incredible flexibility
The basic unit of organization in Notion is the block, which can be a chunk of text, an image, a bullet point, or even a link to another page. Each page consists of these blocks, which can be easily reorganized, moved to other pages, converted into other content types, or generally manipulated in many useful ways. Because of blocks, restructuring information in Notion is way easier than in any other wiki or notebook app.
Pro Does a great job with both notes and to-dos
To-dos in Notion aren't just dot point lists. You can drag and drop them into columns just like Trello (Kanban style), you can have sub-tasks, and you can easily mark things off as completed so they are no longer in your way. Notes are also powerful, with proper formatting and ways to manage and search for them, which makes it a great Evernote alternative.
Pro Cross platform
Works with Android, iOS, Windows, & Mac OSX.
Pro Awesome for wikis
You can easily start writing a bunch of web pages, share it with co-workers and choose whether to publicize or keep your contents private. It's also easy to hyperlink pages.
Pro Amazing view flexibility
You can create different views for a page's content and easily toggle between kanban, table, etc. (As long as the content is able to allow different views.)
Pro Quick and effective search
Just type in a word and you'll have results in no time at all.
Pro Attach files in tables
You can attach files in table cells, which is a feature missing in most spreadsheet-like applications.
Pro Great spreadsheet functionality
You can use calculation/formula, links, attachment, inter-referencing of data from other pages or tables, embed documents and images in the table cells.
Pro Renders Markdown Syntax
Add code blocks, Headers, bullet point, numbered lists, or To-Do boxes by typing using Markdown Syntax (instead of klunkily moving the mouse to formatting boxes)
Pro Less headaches when editing pages
Lets you restore your page to a past edit. Also works with sub-pages and databases. Though it is worth mentioning that it's a paid feature.
Pro Sync with other Apple devices via iCloud, other cloud/email services
It syncs with iCloud, and surprisingly, also with Gmail and possibly other services too.
Pro Built-in
It's a default system app, making it easy to find and use since it is already installed.
Pro Rich-text editing
Allows for simple text formatting and making TODO lists with checkboxes.
Pro Attachments
You can add files to notes and then filter notes by attachment types.
Pro Supports sharing
Pro It's fast, and syncing is very dependable
The app launches quickly on both Mac and iOS, it also syncs quickly (in seconds) and very dependably across different Apple devices.
Pro It remains simple to use with a gentle learning curve
Despite the significant new updates in iOS 9 and iOS 10, you can start using Notes immediately, then try/master new features with ease — definitely a gentle learning curve.
Cons
Con Not very fast using native apps
Can take time if you're switching between lots of pages often as it needs to load the data each time
Con Not always very intuitive
Column filters are not that intuitive to apply.

Con No true backup
True backup can only exist if it's automated and easily recoverable. Else, it's just an outdated copy or useless scrambled data.
Con Designed with teams in mind, and less formatting than Evernote
Evernote may be more individual-oriented and has more formatting and such options available, but whether that affects you is down to personal preference. Try both and see which you prefer.

Con Not yet a new protocol, as it could be! (or could it?)
Think of scuttlebutt or email. the best Evernote alternative would be a "web 3.0" of sorts. Something that would be just a simple file added to a computer and automatically replicated to other computers along with a website and any company could easily pick up the concept and make their own hosting, including some awesome google drive/host of sorts.
Con Cannot export to a format that can be imported again
This makes it obscure and cumbersome to back up your notes as files that could be managed by your backup system. You can export to PDF, but not in bulk; and this isn't the native format that you can easily recover with.
Apple compounds the problem by using some undocumented format for notes. You can, however, back them all up by backing up the files found in ~/Library/Containers/com.apple.Notes/Data/Library/Notes
