When comparing Google Hangouts vs Discord, the Slant community recommends Discord for most people. In the question“What is the best voice chat for gaming?” Discord is ranked 2nd while Google Hangouts is ranked 8th. The most important reason people chose Discord is:
Discord follows the same type of interface design popularised by Slack, which is extremely clean and attractive, and doesn't clutter the interface with unnecessary chrome and cruft.
Specs
Ranked in these QuestionsQuestion Ranking
Pros
Pro Mobile support
Hangouts offers both an Android and iOS app so users can participate from nearly any mobile device in addition to his Desktop.
Pro Screen sharing
Any user can share his screen (or only a specific desktop or window) while still continuing an audio conversation.
Pro Free group video support
Hangouts works with up to 10 participants using video out of the box or up to 15 if you are a business, government or school. It determines who is the primary speaker at any given time, and the camera view automatically switches to that user.
Pro Useful for businesses
Hangouts can scale to become a videoconferencing solution for an entire company, since the software can run on nearly all platforms. In fact, Google itself uses Hangouts as its meeting room video conference software.
Pro Easy to start using
Hangouts is integrated with Gmail & Google+, does not require you to download desktop software, and all chats can take place directly in your browser, significantly reducing the barrier to entry for a new user.
Pro Completely free
Google offers all features of Hangouts completely free. There are business, education and government solutions that increase the participant count to for video calls to 15 and offers support.
Pro Cross platform
Hangouts work on Android, iOS, Chrome OS, web and as a Chrome extension.
Pro Live broadcasting and instant recording
With Google+ “Hangouts on Air”, you can broadcast any hangout to an unlimited audience via your Goolge+ Profile or simply a generic YouTube link. Moreover, any Hangout on Air (public or private) is automatically saved as YouTube video that you can keep for private reference or use in any way that you would normally share a YouTube video. This allows you to record conversations without additional obtrusive software.
Pro Google Voice integration
Allows for a fixed phone number, receiving and making calls. Calling US or Canada is free.
Pro Integrates with Google Maps for sharing locations
When chatting with people while trying to plan a meet up, the share map button can be extremely useful.
Pro Android app does both sms and hangouts messaging
Pro User friendly
Discord follows the same type of interface design popularised by Slack, which is extremely clean and attractive, and doesn't clutter the interface with unnecessary chrome and cruft.
Pro Free for unlimited users
Unlimited amount of users.
Pro Can be used in browser
Users can invite others to join a Discord channel via a web link, which means no installation is required to use the software - which is one of the big typical barriers to entry for social software.
Pro Good 1-click invite system
Discord allows inviting people to a specific channel with a link. Links can be set to expire. Low effort/passive invite mechanics.
Pro Easy setup
You can quickly send invites to people and they can join in using the web client without having to create an account or install the app.
Pro Has low-latency VoIP support
Pro Supports video and text communication
Behaves and looks like Slack for regular text channels, but with the ability to create voice channels as well
Pro Numerous controls for setting member roles.
Deny access, Deny write message, Allow read messages etc.
Pro Ability to create bots
Discord provides an API for creating custom bots.
Pro Open source bots and management tools
Discord has a wide variety of bots for things from airhorn noises to automated server management, to leveling systems for chat. The bot API is open and there are dedicated sites for finding bots.
Pro Game integration
Discord shows which game each user is currently playing, which among other things helps users to form PUGs with minimal hassle.
Pro Dark theme out of the box
Pro Familiar for Slack users
For those that are used to the way Slack (a similar chat client) works, Discord will be familiar in its use, which lowers the learning curve quite a bit for those that have switched or tried Slack before.
Pro Low effort invite mechanics
Pro Android app has push notifications
Pro Syntax highlighting and Markdown support
The support is limited but still exists. It's a killer feature for dev teams.
Pro DDoS mitigation
Discord prevents users from being DDoSed out of games.
Pro Targeting of roles
Targeting roles allows for quickly requesting someone from a group e.g. artist, moderator, etc.
Pro Ability to thread channels
Ability to create channel categories for channels to sit inside of.
Pro Friendly payment policy
Free account have no tangible restrictions.
Premium account is just a way to say "thank you" to developers. And it work for all servers of discord (not as in slack). And it can be purchased by one who wants. In contrast to Slask, where all active members of the server should be "premium".
Pro Language localization
Have localization for many language, including Russian.
Pro Does not allow NSFW related things to be posted unless in a NSFW channel
Cons
Con Poor video call quality
Only goes up to 720p30 + low bitrate.
Con Owned by Google
Con Lacking clients for older versions
Con High hardware usage
Con Not recommended for long sessions

Con Won't work on Windows 8-style UI
As Hangouts uses a browser plugin on the desktop and it doesn't work with Windows 8-style UI, it has to be used in desktop mode.
Con Proprietary software
Discord is closed-source, meaning their code isn't available for inspection or reproduction
Con Based on Electron = eats a lot of ram
Con Some functions cut out and available only with "Nitro" subscription
Con Developer's previous company was sued for privacy violations, among other things
See:
http://classactionlawsuitsinthenews.com/class-action-lawsuit-complaints/openfeint-green-international-privacy-class-action-lawsuit-complaint/
https://www.ftc.gov/enforcement/cases-proceedings/closing-letters/openfeint-inc
Discord's privacy policy also states that while they might not sell your data, a company they get sold to will quite possibly attain said data and thus may be in "more" shady hands.

Con No self-hosting avaliable
Discord is wholly hosted by Discord (the company), you cannot run private instances, and all servers are hosted on their infrastructure. For most people, this won't really impact their usage.
Con Not a generic "team chat" tool
All the UI and the features are aimed specifically at communicating with your gaming team/clan.
Con Very unstable on Linux
Con Anti-privacy license terms
Con Can change "Now Playing" status to something inappropriate
