I don’t see BTTM and ARD as being particularly related and they’re not really intended for the same tasks, and there’s little or no difference between ARD and the built-in screen sharing client for what seems to be the intended usage here.
ARD is for managing fleets of Macs, including pushing out updates, and pushing put command-line commands. ARD can provide screen sharing, but that’s just one of its features. That one screen-sharing feature is entirely equivalent to what the free, and already-integrated screen-sharing app client also provides.
ARD works fine. Yes, there’ve been bugs from time to time, too.
But for remote access from another network and akin to what BTTM provides, and provides transparently, the ARD administrator needs to understand IP networking and IP security to use it remotely, and ro have privileged network access to the associated firewall. Want to learn IP networking and/or VPNs and firewall administration? Use ARD.
Understanding networking? That’s why I keep getting to answer that question. Around how to set up remote access via VPN or port-forwarding. And the security issues and trade-offs of each. Go search for my previous replies.
TeamViewer and ilk are much closer to what BTTM provides and in the way most folks envision, and require less knowledge of IP networking, and can usually work in networks where the user does not have privileged access to the local network firewall.