I don't know what the original poster is seeing in Fedora, but just installing in Ubuntu 14.04 is failing for me. Here's what I get:
$ sudo apt-get install obs-studio
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:
The following packages have unmet dependencies:
obs-studio : Depends: libavcodec-ffmpeg56 (>= 7:2.4) but it is not installable
Depends: libavdevice-ffmpeg56 (>= 7:2.4) but it is not installable
Depends: libavfilter-ffmpeg5 (>= 7:2.4) but it is not installable
Depends: libavformat-ffmpeg56 (>= 7:2.4) but it is not installable
Depends: libavutil-ffmpeg54 (>= 7:2.4) but it is not installable
Depends: libswresample-ffmpeg1 (>= 7:2.4) but it is not installable
Depends: libswscale-ffmpeg3 (>= 7:2.4) but it is not installable
E: Unable to correct problems, you have held broken packages.
It should be noted, however, that I do have ffmpeg, but I do NOT have the repo that was recommended in the instructions. I have 2.6.2 installed directly from the ffmpeg site following their instructions (therefore, able to keep up to date with the latest, and not some horribly outdated repo from god knows where). That's the only thing I can think of that might be causing this issue. I'll likely try adding the suggested repo from the install instructions then re-installing obs-studio to see if that meets the necessary dependencies then, as I have time.
Anyone have any other suggestions, thoughts, ideas, etc.?