Not a problem!
For the Intel i7, expect to get better performance all around. The FX8350 is an 8-core CPU, but the cores don't work together as good as Intel's. You get more out of 4 cores than 8 with the FX. For multimedia, the i7 will match or beat the FX. It also has hyper threading, which helps the 4 cores behave like 8 because each core can address 2 threads. The i7 also uses less power and generates less heat 84 watts vs. 125 for AMD.
For the 780 vs. 970, the 970 is the replacement for 780. It has new GPU technology, faster cores GPU and memory, and has more memory capacity. While the 780 is still a great card, the 970 is still better overall thanks to more efficient processing and more memory capacity. You can run higher resolutions across more displays with the 970. It's a very close race between them, and sometimes the difference will be negligible, but you get more with the 970, plus it's the newest GPU technology while the 780 is still roughly based on the old 6-series (GTX 670-680) GPU.
4 GB is better than 3. The more the better because the extra RAM helps the GPU work faster and process data faster, turning all that data from your CPU into a visible image. It's especially helpful in high resolutions like full 1440p or running multiple displays.
Memory speed is how fast the memory runs, like your CPU, the memory is basically the gateway from the PCIe buss to the GPU. The faster the memory clock, the faster the data is processed. This gives you better performance overall.
Memory bus is basically like an aperture in a camera. The bigger the number, the more data can be processed across the PCIe slot. Although the bus is bigger on the 780 (384 bit vs 256), the 970 is able to get more data across the bus simply because the RAM runs faster in both speed and clocks. This means better performance from the 970.
For bandwidth, think of the memory speed in MHz. The faster the memory can run, the more data can be processed across the bus, which means more electrons being turned into photons. The bigger the bandwidth on the bus (384 vs 256), the more the bandwidth and the more bits can cross it.
Cache for GPU's is kind of arbitrary and not readily discussed. It's more important on CPU's in terms of overall performance.
The 28nm is the size of the transistors in the GPU. The smaller the number, generally the more efficient the processor runs-it gets more done with the resources it has available (shader cores, texture units, pixel rate). The 970's GPU has the same size transistors as the 780, but the Maxwell GPU in the 970 is more efficient, runs raster (over 1100 GHz in EVGA's cards vs. about 980 for the 780). The faster the better.
Shader units, also called "cuda cores" are responsible for turning data into a picture. The more shaders generally the better performance, but that is not always the case. Other things go into actual data resolution than shaders. Although the 780 has more, it still doesn't beat the 970 simply because the 970 has more available memory to utilize. It's a very close race, but the 970 is generally faster. Same for texture units and texture mapping/rate and render units. Pixel rate is the number of pixels can be resolved at one time. The more the better. That's 58 billion pixels per second that are rendered.
For multimedia, it's going to be close between these cards, but for overall performance and longevity and price, I'd go for the 970.