AnyDesk is quite similar to TeamViewer, because a lot of the original developers left TeamViewer to work on that instead. AnyDesk doesn't bother you with on-screen messages/mails to upgrade to the newest version. TeamViewer does not do backwards-compatibility so well. And that is by design as they almost force you to upgrade to their newest commercially licensed (expensive) products and it could happen that you cannot take over the computer you need/want, because of too different versions between your own computer and the one you try to take over.
Can you still spend quite some time having the person on the other end of the line download the latest TeamViewer and install it and possibly open up ports on their firewall, etc. I have been using the free version of Anydesk for almost 2 years now and while the software gets regular updates, there is hardly any "pushing" to newer versions going on. A much more relaxed stance, which I can appreciate. Likely also the reason why those devs left TeamViewer in the first place.