Better build for gaming?

Solution
Let me inform you about the differences:

An i5 will be a quad-core processor and in the 1150 socket, it will be build on the Haswell architecture. Now, the K-series is for unlocked multipliers, which means K-series processors will be appropriate for overclocking.

Now, in terms of gaming any i5 will do the job. What matters is the graphics card. There is a big performance gap between the 960 and 970. Given that any i5 will do the job for gaming, your best choice should now be obvious.

Get the 4440 with an 970. Get a H97 motherboard. If you opt to get a K-series, get a Z97 motherboard.
Let me inform you about the differences:

An i5 will be a quad-core processor and in the 1150 socket, it will be build on the Haswell architecture. Now, the K-series is for unlocked multipliers, which means K-series processors will be appropriate for overclocking.

Now, in terms of gaming any i5 will do the job. What matters is the graphics card. There is a big performance gap between the 960 and 970. Given that any i5 will do the job for gaming, your best choice should now be obvious.

Get the 4440 with an 970. Get a H97 motherboard. If you opt to get a K-series, get a Z97 motherboard.
 
Solution