6

Please post the youtube videos here and I'll see what I can "see" :)
Furthermore, tell me what FPS are you getting on which games….
My friend has the same computer specs as you so I'll play the games there and see how well they run.
:)

This is strange. I can max out both games and get 60+ FPS (but I put V-sync on so it caps 60 fps). You should be able to max out both games and get highest possible fps. My recommendations:
- http://support.amd.com/en-us/download/desktop?os=Windows+7+-+64#amd-catalyst-packages --> install latest drivers…I installed 14.4 and everything is working perfectly
- scan for viruses and trojan
…if that doesn't help, run the diagnostic tool and send me the file.

Have you tried turning down the details and see how that works? Set the settings to high and run the benchmark then.
Most common reasons of low fps are outdated hardware/drivers, viruses, too high detail.
Are you having problems only in Tomb Raider and Diablo 3 or for every game you play?

Then there is a problem in your computer.
1) Check your GPU and CPU temperature and load (are they running full speed and at what temperature)
2) Have you installed any program and got low fps afterwards, or is the low fps problem from the beginning?
3) Check for Pheonix.exe in C:Program Files … or in C:subfolders
4) Try setting lower settings and see how that works
5) Viruses
6) Drivers, mobo…
7) HDD problems: http://technet.microsoft.com/en-us/magazine/dd637756.aspx
As much information as you can provide!

Yes, r9 280x is basically a mildly improved 7970…think nothing of it. It's a normal thing to show it as 7970; Catalyst Control Center will show it as a r9 200 series.
Your mobo is fine, no need to update.
Are you running any program while you play?
Important: Lower settings to medium-high and see if that improves the FPS.

Then you must do benchmarks and cross-check the results with other rigs. Stress test and see if there is anything wrong with any component of your rig (hardware). If you are getting lower fps then other people with same rigs my educated guess would be:
-Virus
-GPU drivers
-Catalyst control center is poorly optimized(I know when I set different filtering it went Harlem Shake)
-Set the power mode to High Performance
EDIT: Create a thread and let other people help too. Maybe other mis fortunate people with same problems and solutions.