Still, is it possible that some web pages can recognize the higher resolution of the newer iPads and transmit imagery and video at that higher resolution (more data)? Or, does the newer iPad with 4G do things in the background that were not possible with earlier iPads and slower cellular data?
...
...Is it possible that the new iPad has icloud sync where the old one did not? I wonder how much data this consumes?
Rather than the type of device you are using, web sites can recognize your data speed and adjust the quality of the video to match. It's a good idea to go through settings for sites and video apps, setting your default video quality to override this feature. Pick the lowest bandwidth with the quality you are satisfied with. I find 480P satisfactory for viewing on my iPad and iPhone.
For sites without preferences, the video will usually have a quality control somewhere at the bottom, if you remember to switch to a lower quality you can save a considerable amount of your data allowance.
With iOS 5 and even more so with iOS 6 there are a number of services that will sync automatically over your cellphone connection. Check your iCloud settings. By default, the heavy hitters like Photo Stream and Documents & Data will only sync over wi-fi. Most of the others will sync over cellular, but don't use up a lot of data (with the possible exception of Mail which may contain large attachments).
Under Settings > Cellular Data you can turn ON/OFF cellular syncing for some of the background services under the Use Cellular Data for: section. iCloud Document syncing can be turned ON here. Photo Stream does not appear to have any cellular syncing options. It is wi-fi only.
You can also turn of LTE service here, in case you want to self limit your speeds. While it won't stop the iPhone from syncing stuff in the background, but it will slow it down, which in some cases may result in less data use.
Or you can turn off Cellular Data altogether, and only turn it on when you out and about and, actually need it. Inconvenient, but the ultimate in data use control.