Hardware looses stability over time. Especially PSU's.
Battlefield 4 uses your gfx in more ways than ARMA and Skyrim ever could. Try underclocking your gfx + cpu with 10% below stock and see if that helps. If it does that could suggest unstable overclocks or heat/PSU issues.
Just to add to all this and try and help. Have you checked your PC inside for dust as this could also do this. Just turn off all power to the PC and unplug PC, open it up and blow dust out of PC with a can of air.
Other then this I would check your windows as well just to rule it out...
Test your windows for errors as a clean windows install does not always make a stable windows.
NOTE>>> Running SFC does not guarantee the crash will not happen, but it will ensure it is not because a windows Dll or file is corrupted in windows.
This works in all windows O/S vista Win7, Win8 and Win8.1 windows system file checker :] Copy and past this to note pad and put it on your desktop. As open programs can give you errors when you run this.
...... sfc /scannow ..... ever hear of it if not your going to love this .... it will inspect all the important windows files as well as the windows DLL files. If windows system file checker finds any issues with the windows files and windows DLL files it will replace them / try to fix them. This little tool as well as the event viewer on a PC saved me and fully helped me fix my BF4 issues as well as saved me many a format since I found it. This is the best toy they ever put in windows 
For win7 go to start/ bottom left screen / windows globe .. Right click in search type cmd and right click cmd pick run as administrator.
For win 8.1 right mouse click start bottom left of screen / windows box and pick command prompt administrator.
1 - Open administrator command prompt and close web pages and programs like Origin, Steam etc.
2 - Type or copy and paste in sfc /scannow and hit enter, This takes 5 min to 15 min SSD vs HD
3 - This can go one of a few ways ..... no errors ... it fixed some errors ..... could not fix all errors...... does not finish checking and errors out ....... and the last one could not fix errors at all :/
4 -After its done REBOOT PC and Run sfc /scannow again even if you had no errors the first time or had errors, could not fix ... run sfc /scannow again and when its done a second time reboot. You need to do this a and get no errors 2 x in a row ...
5- So if you ran it 2x and no errors your safe you can stop. If you had errors first time but not the second then run sfc /scannow again and when its done reboot. You need to get could not find any errors 2 x to be safe. If it still finds errors try and run it a few more times until it finds no errors 2x AND ALWAYS REBOOT BETWEEN RUNNING sfc /scannow
6 - If you get a message indicating that it can not be repaired and you ran sfc /scannow more then 3x in a row on win vista or 7 mm you need a format or try repair win 7 :/ But after format or repair and all updates are done run sfc /scannow to make sure your windows is stable same deal 2x error free reboot between them.
If your O/S is Win8 or Win 8,1 then you can run the next few command lines in administrator command prompt. Sadly this does not work for win vista or 7 :/ Note: After you run each command line Reboot PC.
This next part of windows scans is only for windows 8 & windows 8.1
Reboot PC after you run each command line and close programs and web pages. And same deal as above run command prompt administrator.
1- This command line will scan the health of your PC.
dism.exe /online /cleanup-image /scanhealth
2- This command line will restore the health of your PC and you don't lose anything on your PC .
dism.exe /online /cleanup-image /restorehealth
Note: If you get errors with the two command lines above and it cant be fixed with second command line and if you are on windows 8.1. Then use third command line but be warned it could take up to two hrs to fix your PC but it will save you a format. I had a friend test this on a PC with errors when it could not be fixed with second command line.
This next part of windows scans is only for windows 8.1
And same deal as above run command prompt administrator.
3- If restore heath gave you errors then you can always try this command line.
dism /online /cleanup-image /startcomponentcleanup
4- If you get Error 0x800F081F with the restore health scan then run this command line. After you reboot your PC then run third command line to be sure your windows is fully stable.
Dism.exe /Online /Cleanup-Image /AnalyzeComponentStore
