Depends on the games you play really but if dcs or arma are high on the list of games you play then intel is where you probably want to be for now.
AMD is awesome price to performance especially in newer games. I know because I had an 8350 and my brother had a 4670k. I had a 7950 oced and he had a 7970 no oc(I sold my 7950 for more than his 7970 in the end lol) then we both got 290s. We sat next to each other for 2 years comparing fps in games, and there were only 4 games that he had significantly better fps: arma, dayz, skyrim, and dcs world. Now this wasnt always consistent but in critical times where you really need the frames the 4670k would definitely pull ahead.
AMD takes a bit of work sometimes to get the best out of it but Im a tinkerer so its not as if I wouldn't have oced it anyway. In games like crysis 3, far cry 3, far cry 4, BF4 basically any game that isnt shite for optimization it is a great option. Single threaded and single core intensive games and it starts to lag behind.
IF you had an AM3+ mobo still Id say just get an FX series chip. Seeing as how you want to upgrade AND need a new mobo, its easier to say intel. I loved AMD and will always buy their GPU's, but depending on your budget a 4690k will be a huge upgrade. I mean I launched DCS yesterday and getting 55-80 fps on the ground is huge especially with headtracking and landing is amazing without 15 fps lag city.
In answer to your question an 8350 will be a large improvement over your 965 even in single core, especially stock vs stock. For 50 bucks moreish a 4690k will be an improvement in GAMES such as dcs world and ARMA 2/3. But that 50 bucks also can go towards a great ocing mobo. These are US price estimations unfortunately.
The principle is: if you're like me and you play only dcs or arma 3 then intel is kinda the way to go. But yea 1-5% increase is not at all true. I had my 965 be at 4.0 and still noticed an almost 15 frame improvement in arma 2 dayz, stock 8350. Good luck!!