How I see Discord:
FREE ( That is a plus. )
Cannot be DDoSed, doesn't lag ( Okay another plus if it is true. )
Easily accessible anywhere you are through desktop app, regular browser or mobile app ( TS is also easily accessible. )
Can message people when they are offline, see what games others are playing ( Sounds okay )
Notifications and mentions, just like on the website ( We have a website for that. )
Much more secure (no alts, VPNs or proxy trolls etc) ( Alts/trolls are easy to ban on TS since you need to register to get permissions. )
Better chat and voice quality ( Really? Not in my opinion. )
Better group management ( You mean Staff ranks/Donator ranks or something else? )
Bots with custom functions like custom commands, activity tracking, quizzes, tons more ( Don't need that to be honest. )
Much better looking (TS looks like it came bundled with Win98) ( Who cares? If it works it works. )
Multimedia extensions (embed images, videos) ( Website? )
Frequently updated with new features ( More things that you never use in my opinion )
We can have a widget on the front page showing who is online ( Is that necessary? )
Everything else ( Like...? )
None, you have to overcome your fears, enter 21st century and let TeamSpeak go ( Uh please no! )
Donators can have private TS channels.
Easy to see if everyone follows Rule 1.8.
People can have custom badges/descriptions and/of avatars.
Knowing Discord a bit you will need plus/minus 60 channels, is that possible?
Easy to moderate for Staff. Discord will be a hell. Well, that's Staff's problem.
Channels for groups.
Voted to keep TS.