The short answer
BeyondDisplay is the simplest choice when you already have two compatible Macs and only need a local extended display or mirror. It is free, requires no account, and uses the Wi-Fi, Ethernet, or Thunderbolt connection you already have.
Duet Display covers many more devices and workflows, including iPad, iPhone, Android, Windows, remote desktop, and drawing features. Luna Display supports older Macs and iPad workflows through dedicated hardware that stays connected to the primary computer.
BeyondDisplay is also expanding beyond Mac-to-Mac: an iPad receiver is in development and nearing completion. Until it is released, the downloadable version still requires two Macs.
A free Duet Display alternative for two Macs
If your goal is simply to use another Mac or MacBook as a second monitor, BeyondDisplay covers that Mac-to-Mac workflow without a subscription. Install the same app on both Macs, choose Extend or Mirror, and start the connection from the Mac whose desktop you want to expand.
Duet Display is the broader option when you also need Windows, Android, remote access, or drawing-tablet features. BeyondDisplay is the more focused alternative when both computers are Macs and you want the display traffic to stay on your local connection.
A Luna Display alternative without a hardware dongle
BeyondDisplay can turn a Mac into a second display without buying or attaching dedicated hardware. It connects through Wi-Fi, Ethernet, or Thunderbolt Bridge and does not require both Macs to use the same Apple ID.
Luna Display remains the stronger fit for older versions of macOS and for its established iPad workflow. BeyondDisplay currently requires macOS 12.3 or later on both Macs; its iPad receiver is still in development.