[noja]

Both of those sites are for checking remote servers. BadSSL is for checking what your client browser behavior is.

[Symbiote]

But SSLLabs does have a client test, it's even linked to from the BadSSL dashboard page.

https://www.ssllabs.com/ssltest/viewMyClient.html

[watter]

It took me going to this page to understand what was going on, I assumed it was a web server test. The report was more pratical too, telling me what I'm protected against, not just a bunch of yes/no things that I have to go reference. I'm on a phone in portrait mode though so maybe it is just a formatting thing.