Does anyone here prefer an I7 6800K to an I7 6700K? Do you consider it to be a worthwhile difference?
For overclocking the 6800 has a clear advantage. Well that's if you're looking at multitasking.
Nope. For gaming, stick with the 6700k
The 6700k uses a newer chip architecture (Skylake). The 6800k Is Broadwell-E, the generation before.
The main difference (apart from architecture) is the 6800k is a six core chip with hyperthreading (12 threads) and the 6700k is a quad core with hyperthreading (8 threads).
For gaming, the 6700k is the clear winner. But for the money, you might want to drop down a level to the i5-6600k, which loses the hyperthreading, but has tons of overclock potential. PC Gamer (and Maximum PC) puts the 6600k as the current best pick CPU for gaming (price/performance). Save the money on the CPU and reinvest it into your GPU.
If you are going to be doing CPU intensive stuff, like video encoding, then the 6800k wins hands down. the 2 extra physical cores and 4 extra threads will make short work of whatever you are doing.
http://www.pcgamer.com/intel-core-i7-6800k-review/