Is there an equivalent of Windows' Remote Desktop?

I would recommend X2go. It's very similar to RDP and highly efficient even over low-bandwidth, high-latency connections. Clients for all systems, including a plugin for Firefox, etc. It works over ssh and integrates with PulseAudio so you can use VoIP, for instance. Read more on http://www.x2go.org

The x2go client requires a session command to execute upon logging in. For example, to use Unity 2D, use the session command: gnome-session --session=ubuntu-2d. This was found by looking in the file (on the host) /usr/share/xsessions/ubuntu-2d.desktop and copying value of the Exec=... line. If you want to use some other session, you can use the value from another file in /usr/share/xsessions/, but it seems that anything requiring 3D acceleration will not work.

Chrome Remote Desktop BETA

★★★★½

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This is a Chrome extension by google, which installs a plugin in chrome for enabling remote desktop sharing. The sharing is much simpler compared to other solutions, and is easy to setup.

Chrome Remote Desktop BETA allows users to remotely access another computer through Chrome browser or a Chromebook. Computers can be made available on an short-term basis for scenarios such as ad hoc remote support, or on a more long-term basis for remote access to your applications and files. All connections are fully secured.

In general, xrdp will do what you want. And is compatible with many RDP clients out there.

The drawback is that Unity, the default WM in Ubuntu, no longer supports it. I believe, although I've never tried it, that it works with GNOME.

For my personal use, I just installed MATE desktop (as it has less "flair" then GNOME) and configured Ubuntu to use that whenever remotely logging in.

See here for information on setting it up (This answer uses XFCE for remote-desktop. You may choose something else):

https://askubuntu.com/a/592544/595510