When comparing Gnome 3 vs Budgie, the Slant community recommends Gnome 3 for most people. In the question“What are the best Linux desktop environments?” Gnome 3 is ranked 6th while Budgie is ranked 8th. The most important reason people chose Gnome 3 is:
Every aspect of GNOME 3 has been crafted to fit together as a harmonious whole, so that it offers a consistent and integrated experience.
Specs
Ranked in these QuestionsQuestion Ranking
Pros
Pro Clean UI
Every aspect of GNOME 3 has been crafted to fit together as a harmonious whole, so that it offers a consistent and integrated experience.
Pro Simple and easy to use
GNOME 3 has been designed to make it simple and easy to use. Press a button to view your open windows, launch applications or check if you have new messages.

Pro Highly customisable
Gnome Extensions offers an easy way to extend the built-in functionality.
Pro Powerful search
A powerful search feature lets you access all your work from one place.
Pro Does not get in the way
GNOME 3 lets you do the things you want without getting in the way. It won't bother you or badger you with demands, and it has been designed to help you comfortably deal with notifications.

Pro Keyboard friendly
It's (mostly) usable without touching a mouse, so you can keep your hands on the keyboard.
Shortcuts can be defined in the gnome setting.
There are even more shortcuts available when using the gesetting or dconf tool, e.g. switch to desktop 5 to 9.

Pro Great for high dpi displays
Adjustable scaling factor makes it great for high-resolution laptops and far away TVs.
Pro Very productive
With a clean layout and well-thought keyboard shortcuts, Gnome 3 is simply the best for people looking to be productive with their computer.
Pro Online account management
GNOME 3 integrates with your online accounts, so that all your data can be accessed from the same place.
Pro Adheres to standards
Allowing for interoperability and shared technology for X Window System desktops.

Pro Easy theming
Changing the look (and feel) of Gnome Shell is easy, shell theme, icon, windows and graphical elements (gtk) individually for each user.
Mostly it's installing some packages or unpacking some archive to a themes folder and using selecting the new theme in e.g. gnome-tweak-tool.
There are a lot of really good themes on DeviantArt.

Pro Great task manager
The GNOME Task Manager is great, showing all open processes with every needed detail. For each process you can see the amount of memory and processing power that it's using, along with the process priority.

Pro Wayland support
Gnome is the first desktop environment that uses Wayland as default instead of X server. X server is only optional currently.
Pro Fallback mode offers a classic look
For people looking for older, more classic looks, Fallback mode offers just that. Ubuntu users can have this option by installing a package called "GNOME-Session-Fallback." In the future to be released GNOME 3.8, the Fallback Mode will not be included, so this is really not a long-term solution.
Pro Gnome-Tweak-Tool and Extensions are great
Gnome may seem bland out of the box but, the Gnome-Tweak-Tool is awesome.
The Gnome-Tweak-Tool allows for easy desktop tweaks and other control functionality, and that these features can be activated with just a click.
Pro Touchscreen friendly
It works well with any touchscreen-enabled system, including newer laptops, even to the point of including a well-designed on-screen keyboard.
Pro Integrates with most Google Services
You can use your calendar, drive, contacts and most of Google services with Online Account option. You can show your Google Calendar events on the Gnome's default calendar app, Nautilus (Default file manager of GNOME) almost fully integrated with Google Drive and even you can read your PDF's with Evince (the default built-in PDF reader in GNOME).
Pro All the major players in the Linux ecosystem have finally collated on Gnome.
Red Hat default = Gnome
Fedora default = Gnome
Debian default = Gnome
Ubuntu default = Gnome
Opensuse default = Gnome
This doesn't mean the others go away, it just means there is a colossal community and industry backing behind Gnome.
The point whether or not it being technically the best option is now off table and irrelevant. It is now the de facto standard. Like it or not.
Pro Built from scratch and integrates into current technolgies
Budgie is built from scratch to integrate with the Gnome stack, this way hopefully having more stability by utilizing technologies that have a lot of community work already behind them.
Pro It's minimal and gorgeous
Seriously.....Look at it.....
Pro It's maintained by a dedicated bunch of folks with an eye for detail.
Pro Very Lightweight
Runs well on low-end hardware and gaming PC’s alike.
Pro Can emulate Gnome 2 desktop look
The Budgie desktop can emulate the classic Gnome 2 look.
Cons

Con Extension system is weakly integrated into the environment
Backward compatibility is not guaranteed and extensions seems like second class citizens in the GNOME environment.
Con Tightly coupled to its window manager
If you're looking to run an alternative window manager, like XMonad, you're pretty much out of luck.
Con Limited customization
To modify anything beyond the wallpaper requires third-party software.
Con Heavy on RAM
It is the DE that needs the biggest amount of RAM.
Con Some GUI controls are much larger than on other desktops
This is wasting screen space on non-HiDPI monitors.
Con Some settings are not where the user would expect it
E.g. it is not possible to change the keyboard auto-repeat delay or rate from the usual All Setting > Keyboard like, for example, in Unity.
Many settings are considered "tweaks" and require installing a separate utility to adjust.
Further still, some settings are buried in a dconf database.
Con Depends on systemd
Some people don't like systemd but it is part of most modern distros anyway.
Con Longtime support is hard since every few years GNOME changes its own standards.
Everytime something is complete GNOME breaks itself:
Icon naming changes almost every 3 years : once gtk icons were named stock_edit then gtk-edit then edit-edit and currently edit-edit-symbolic
- App icons change also every few years currently they get renamed to an android like scheme eg: org.gnome.Photos.svg instead of gnome-photos.svg however this breaks all common standards esp. since filenames on linux are case sensitive.
GNOMEShell extension also break on almost every release.
Currently Gtk3 has been stabilized however they are already working on GTK4 and 5 so in the worst case your desktop will need to run and support 4 GTK-toolkits at the same time.
Con Slow
GNOME 3 desktop environment is kinda slow on some Linux distributions
Con Poor 'drag and drop into application' capability
Difficult to drag and drop a file into an open application.
Con Hefty (Lots of dependencies)
Gnome 3 in the current state is heavily weighed down by having a lot of functions as requirements, rather than options. You MUST have their email client, calendar, and more installed as the environment relies on them directly for basic functionality. Which is absurd as most other DEs don't require a specific calendar program just to tell you what day it is.
Con Rather insane method of wallpaper slideshows
Most DEs and WMs allow the user to simply point to a directory, and use pictures from there. Gnome 3 requires the rather asinine idea of building an XML file to accomplish the same thing.

Con Non-intuitive use paradigm
Con Inconsistent desktop
As of GNOME3, some applications have ClientSideDecorations while other use normal Titlebars, this also affects usablity since both Decorations do different things if you left, right, or double click it. Same goes for Menubars. Some Apps follow the GlobalMenu in the GNOMEShell while others don't.
Con Less light weight than you would expect
Budgie has a nice and simple style, but the memory usage is quite high after booting. Thankfully, the lead developer is working to remedy this.
Con Sometimes buggy
Budgie can sometimes be buggy.
Con Still in development
Budgie is still young and in active development, so it may not be as stable as many other desktop environments.
Con Does not properly support multi monitor
Having two monitors works, but it's not perfect.
Con Issues with proprietary drivers and Mutter
Mutter causes issues with screen tearing and microstuttering in most applications especially with NVidia GPUs.
Con Very hard to install
Installing in distros that are not ubuntu based can be hard.