I have never noticed any difference regarding clarity between those dates.
The clarity differences you get are based upon the wind and surge. The more northeasters, the more sand and particulate matter moves around in the water and the vis goes down. Never bad vis, just not as good as other dates.
It can go either way, it depends on the weather pattern. Statistically speaking you are more likley to get a front pass through in December than November, so it is more likley that December may have that issue more so than November.
The water temperature is pretty much the same, maybe a degree, two at the most difference. I would Google the question for the exact answer. I have not seen any water temp below 78 in either case, if that low. Mostly around 80.
The temperature issue you will notice is the air temperature if a front passes through. The air temperature can get cooler in late December than November.
We travel both of those times every year and really enjoy it.
If the northeasters are blowing, you get to dive the south side, which we enjoy and don't see as much of.