I must sound like a broken record to people here but this is how I answer questions... I'll start off by briefly describing each of the processors to spur discussion...
The Intel® Core™ i7-920 Processor has a base frequency of 2.66 GHz and a turbo boost frequency of 2.93 GHz. It is a quad-core processor with an 8MB cache and is hyperthreaded to 8 logical cores.
The Intel® Core™ i7-3770K Processor has a base frequency of 3.5 GHz and a turbo boost frequency of 3.9 GHz. It is a quad-core processor with an 8MB cache and is hyperthreaded to 8 logical cores. If you care, this processor is unlocked (you can easily modify the clock multiplier for better performance, assuming your cooling can handle that).
I'm assuming you meant, when you said "i5 2700k", the Intel® Core™ i7-2700K. The only important differences between this processor and the Intel® Core™ i7-3770K Processor is the fact that this processor is slightly slower in both single- and multi-threaded tasks and uses a little more power.
Okay, now we've hit troubling waters. I'm going to briefly describe the AMD Processor you listed but keep in mind this fact most people don't understand: clock speeds in Intel Processors and AMD Processors CANNOT be directly compared. For example, if we had two processors of the exact same specs and a 3 GHz clock speed but one was from Intel and one was from AMD, the Intel Processor would significantly outperform the AMD Processor. The pro that usually comes with many AMD Processors to compensate for this speed disadvantage is more cores.
The AMD FX-8350 Processor has a base frequency of 4.0 GHz and a turbo boost frequency of 4.2 Ghz. It is an octa-core processor with an 8MB L3 cache and a 4x2MB L2 cache and is not hyperthreaded so it has 8 logical cores.
Now let's analyze all this information to answer the question...
These are all great CPUs, however a "best" CPU for this system can only be chosen when it is known what it is going to be used for. For example, if the system is going to be used to do general tasks, such as school related tasks, with some moderate to heavy gaming, the best option would be to pay $100 to upgrade to the Intel® Core™ i7-2700K. The extra $50 to upgrade to the Intel® Core™ i7-3770K is not worth is, seeing as the Intel® Core™ i7-3770K only sees an average of a 3% performance increase over the Intel® Core™ i7-2700K.
If the system was to be used mainly for hardcore gaming, the best choice would be the switch to the AMD FX-8350 Processor. If you are playing hardcore games such as Battlefield 4 (games of this kind are able to utilize 8 cores) on higher settings, the 8 cores in the AMD FX-8350 Processor will increase performance over the 4 cores in the Intel Processors we had to choose from.
Final verdict...
Seeing as the AMD FX-8350 is at no extra charge to you, that is the processor I personally would go with because I game a lot.