Basically, they don't make triple-channel kits of memory for my LGA1366 i7-980x processor anymore. But they do make quad-channel kits for the new 2nd generation i7-3930K processor. Is this memory compatible with my older processor? I plan on buying a quad-channel kit and using only 3 sticks. Is there any actual difference between memory based on generation of processor?
There is no real notion of "memory based on generation of processor". The memory specs are the memory specs, and they're really independent of the processor generation. Some processor generations require new RAM specifications; some don't. For example, the Ivy Bridge mainstream processors -- e.g. i7-3770K, which is not to be confused with Sandy Bridge-E, the 3930K you referred to -- use the same dual channel DDR3 memory that has been in use since at least the Core 2 era (older than your LGA1366).
The real question you should be asking is whether quad-channel memory can run in compatibility mode in a triple-channel configuration.
My understanding is that, overall, memory sticks are not specifically manufactured to run in a specific channel configuration, except, I think, in the case of dual channel. So the general rule is, if you have dual, triple or quad channel memory, it can probably be made to work with any dual, triple, or quad channel motherboard that otherwise supports the timings, clock rate, capacity (amount) and generation (e.g. DDR3) that the particular RAM module has.
However, there are some memory modules that are manufactured with less rigorous specifications / procedures to meet a lower price point. These modules can sometimes fail to work in channel configurations of more channels than they are advertised for. So for example, certain models of Kingston RAM that are specifically "dual channel" will not work on triple or quad channel configurations. However, quad channel modules should always be able to go "down" to triple channel.
(and further down in the quad-channel section):
The first paragraph, as I interpret it, tells me that the system will tax the memory modules "harder" in higher channel configurations, which might explain why certain cheap dual channel RAM will not work in triple or quad configurations, yet quad configurations tend to work very well as triple channel. The second paragraph says that, on a quad-channel motherboard, if you plug in four quad-channel memory modules and then remove one (or insert any multiple of 3 sticks that is not divisible by 4), the system operates in triple channel mode. So that tells me that for certain, quad-channel RAM can operate in triple-channel mode.
There will be no difference between the memory modules in a "quad channel" kit and using only three memory sticks (modules) compared to a "triple channel" kit.
The kit is basically just a group of memory modules that came off the production line at the same time and so should have exactly the same timings and other features as each other module in the kit. It is entirely possible that you could go into a shop, buy three of one type of memory module and be given three sticks that came from the same batch but there's a chance you'd get one or more from different batches.
Having the modules from different batches is not necessarily a problem in itself, the only problem comes if they came from batches before and after a specification change whereby one module might be working to slightly faster timings compared to other modules.
Even then having these difference may not affect the system in a way that you would even notice, it might be down to loosing a couple of MB/s on a benchmark.