Personally I hate Slack, it never works on my PC because of their organizations/workspace system, where you need a separate account for each community you are in. Also, it's really buggy and login often doesn't work, or switching accounts breaks things.

Telegram has a really good mobile app, and their BotFather makes it easy to create custom integrations. They display nicely a lot of notification formats (text/html/markdown) and it's free.

Slack is too bloated to simply use for notifications.

I can only talk about the Slack integration story since I never worked with the Telegram API, but over the last couple of years it has become an incredible mess. There are various ways to do the same thing, different permission models, deprecated endpoints without clear alternatives... It has become a pain honestly.

I think many users choose Telegram, as it's really simple. Slack is usually slightly more work to setup, e.g. creating the slack bot for it. I'm using Slack ware more than telegram, but I guess both work.