Both C2 and C3 support multiplayer.
C3 is the latest version of Construct that works on the vast majority of devices and platforms (PC, Mac, Chromebooks, mobiles, tablets... it goes on!) whereas C2 only works officially on Windows PCs.
In terms of practical end-use features, C2 and C3 are currently tied - as they both use the same runtime (the underlying engine that powers Construct games).
However C3 has a dramatically improved UI and tweaks to existing features (such as the array editor, which provides a visual aid - something lacking in C2) - the full list can be found here.
Whilst they seem very similar now, C2 to C3 represents a paradigm shift towards a more flexible "tool". I'm remiss to call C3 a tool as I personally view it as more of a service, and C2 as a product. This is reflected in new export features (C3 offers automatic Android app generation and official IAP plugins), and subscription based pricing model; which allows the devs to iterate on existing foundations.
Moving forwards, C3 will receive an updated runtime that will offer better performance and capabilities, making it the logical choice if you have ambitious ideas that will push the engine to its limits.