Hardware:
00:02.0 VGA compatible controller: Intel Corporation 3rd Gen Core processor Graphics Controller (rev 09)
01:00.0 VGA compatible controller: Advanced Micro Devices, Inc. [AMD/ATI] Wimbledon XT [Radeon HD 7970M] (rev ff)

So I'm using radeonsi with PRIME and latest mesa git, recent llvm 3.6 revision.

I foolishly deleted the old Unreal Engine Demos so I can't make a recent test, but they worked decently last time I checked.

Now the Unreal Demos have been updated to UE 4.5: https://wiki.unrealengine.com/Linux_Demos

"Tappy Chicken": Works fine on intel and radeonsi.
"Shooter Game": Works fine on intel, but shows only game HUD and text on radeonsi
"Light Room Interior Day Demo": Works fine on intel but is completely black on radeonsi

Apitrace says the only problems are:

$ DRI_PRIME=1 glretrace Lightroominteriorday.trace
882: glDebugOutputCallback: Medium severity API other issue 1, FBO incomplete: no attachments [-1]

0 4096 glXSwapIntervalMESA(interval = 0) = 0
4096: warning: unsupported glXSwapIntervalMESA call
context mis-match in pipe_sampler_view_release()
Rendered 191 frames in 13.88 secs, average of 13.7608 fps

Here is the trace from which I got the above output: http://haagch.frickel.club/files/Lightroominteriorday.trace.xz
It renders fine on intel, but only black on radeonsi.

(Careful: When creating a trace on intel, the engine will use glCopyImageSubData which is not supported on radeonsi. When creating a trace on radeonsi it will not.)