Another variable with iGPU performance is the motherboard used, believe it or not. Some motherboards can over-volt the iGPU and overclock it automatically, while other motherboards can't. Primarily, you want a Z87 platform for iGPU for max performance, but the difference generally isn't worth it. For instance, asus motherboards have iGPU voltage offset and that basically applies higher iGPU clockspeeds with higher voltages. Whereas H87 and H81 platforms cannot do this. Again, it's not worth changing platforms JUST for this. But it's another variable.
Honestly, i'd say the games you're looking at are not too demanding, and you'd probably be fine. Minecraft strikes me as requiring more CPU heft, so that could make an argument for the 4330. However, you may need to lower the resolution and/or details a tad in those games. There is also not a large difference between the 4400 and 4600 at default iGPU clockspeeds. IF the 30$ is important to you - or if you can better allocate it elsewhere - i'd say just get the HD4400.