Emacs

So I can do terminal stuffs in Emacs, instead of having to open another terminal window

Terminals are helpful?

It's not clear what you're interested in here. Why use a terminal in emacs as opposed to a separate program? Why these over eshell?...

For me: To run commands such as brew.

I get your point. I messed with eshell for a while, then used vterm. In the end I just hard wired a swaywm key to a scratch terminal wihch toggles an alacritty instance. I can copy and paste in it fine : in short I find it easier to do "terminal shell things" in a "real terminal" but I can see why others prefer to stay inside emacs. Occasioanlly I'll use a terminal inside emacs via projectile as its quick to open a terminal at your current project location.

Vterm: none that I can see

Eat: it's awesome, very good and fast and mouse input works out of the box

They are just another terminal emulator, not much else. So the point? Not much if you use emacs as just a text editor.

If you are more intergrated into the emacs environment there are features that you may find useful such as directory tracking. Worth checking out their project pages to see if they make sense in your work flow.

Use same keybinds as in other Emacs buffers to manipulate the text e.g. search, copy/paste, folding; matching theme; project context; etc.

I used both extensively but the both are faster than term or shell.
Vterm is the fastest and most correct about handling key events.
Maybe term will get similar improvement as vterm in the future. This is such a basic thing that most other IDEs also seem to support properly.

Fun thing is I'm currently using Emacs mostly for vterm, lol. I code in another app (works better on my current project), I've switched from org-mode to LogSeq (long story).

Well, ok, also magit.

If you are a web developer, you will notice that modern toolchains tend to assume interactive terminal. Most of them can be run in compilation-mode, but some do not function without interactivity. For example, you will probably need a terminal when scaffolding a project using a CLI.

Being able to do emacs stuff in my terminal and terminal stuff in my emacs while sharing the same kill ring and other similar kinds of state.

I use M-x shell for most shell commands. This provides "infinite" scrollback, easy to grab output into the kill ring, etc. It's kind of like a temporary notebook (though easy enough to save). When I need a full terminal such as gdb -tui, I use a more traditional terminal emulator like gnome terminal.

You mean "as opposed to using term.el" ?

Performance, mostly. (I'm still using term myself, but suspect I'll switch to eat at some point.)

None if you don't care for terminal emulation. You can use M-x shell and have a much better experience.