Multiplayer game probably better in Unreal Engine, because it comes with a built-in server-side solution. Plus if you want things like matchmaking, friend list, badges, achievements, leaderboards, etc. Unreal Engine has got a free community-developed Steam bindings plugin or you could even use the Epic Online Services, which is free for use with Unreal Engine.
I've got 6 years with UE and 15 years programming in general. You can trust me that my time efficiency is worth the cash. :-) Let's speak about details.