Is great out of the box, but can be customized to your heart's content with custom CSS.

You can use any sync service you want, and your notes won't disappear even if Obsidian does.

No limitations in terms of usability. All the features of the program are available for free.

Daily Notes plug-in, when clicked, generates a new note with the current date. Great for journaling and reduces friction in your writing habit.

You can create a custom template for your Daily Note.

When you hover on an internal [[link]], you get to preview the note without opening it on a new pane.

Page preview plugin must be enabled.

Panes in Obsidian can be split infinitely and resized, and they make cross-referencing multiple notes a breeze.
Panes can be pinned to keep its content or linked together so they can show different views of the same note. Combine panes to set up your powerful workspaces.

No support for filtering and changing centers yet, though.

Easy and fast format [[link]] and shows the pages that link to the page you are on in the backlinks panel.

Makes it easy to learn.

It's becoming more powerful everyday, it seems like they add many functions within several days.

You can change the theme with custom CSS.

Supports these necessary features for Comp. Sci. and Math.

A plugin that, when clicked, surfaces a random note from your vault.

Easily turn your notes into simple yet sleek powerpoint-style presentations by enabling the Slides plugin and adding the --- separator.

This is a big difference, as having to read through long-form texts laden with [[links]] gives friction.

Linking notes is a game changing feature. Very easy to use and link notes. Their implementation of markdown doesn't deviate from the standard form of markdown and so the same files can be used by other markdown programs without any consequence.

A feature unseen in other tools.
From the help doc, "This can be useful when modifying a lot of lines in the same way, for example putting - at the beginning of multiple lines to turn them into a list, or appending [[ to a series of links you’ve copied from elsewhere."

The app doesn't frustrate the user - the built-in help is excellent.

The onboarding consists of well-written help documentation (saved as a vault) served in small chunks and organized systematically so that you become familiar with all its features as well as get hands-on experience in real time.

A Vault in Obsidian is like a database. Internal links and files are not shared across Vaults. Each Vault is opened with a separate instance of Obsidian. Each Vault can have its unique app settings and plug-ins. Useful if you have distinct/unrelated projects or "data spaces" requiring different workflows and data relations.

Ability to tag-as-you-write and find each occurrence of a tag in the entire vault makes it very easy to organize and retrieve notes.

In Obsidian, pane = window = note = page

Obsidian allows you to open as many notes as you can fit concurrently in your screen. You can split a pane horizontally/vertically. You can lock/link panes so they scroll in sync, useful for and edit & preview modes.

There is no mobile app yet.