Cartoon Network HD looks great. Animation doesn't require as high of bitrates which is another reason why it's infuriating that Verizon hasn't added this channel yet. It would only need half as much QAM space as the typical HD channel! It's ~8 Mbps on Time Warner most of the time and it looks to be basically Blu-ray quality until the occasional really fast action animated scene (then there is indeed some macroblocking).
As for most of the other channels, it's a toss-up. Almost all HD channels are distributed natively as MPEG-4 on satellite now so Verizon and all other cable providers with MPEG-2 boxes MUST re-encode almost every channel. The bitrates are comparable with most FiOS TV channels.
Verizon does still have a handful of channels it re-encodes at bitrates higher than ~13 Mbps. Some of these include EPIX & EPIX 2, HDNet & HDNet Movies, A&E, and History.
As A&E Networks are only 720p there's not much of a quality improvement there, higher bitrate or not. EPIX and HDNet are the best looking channels on Verizon but Time Warner doesn't carry them anyway.
Here's a few screenshots of Cartoon Network HD on Time Warner (click for full 1920x1080 .png):
If you're stuck with FiOS TV and would like some more screenshots from HD channels you can't get like BBC America, Cooking, G4, Game Show Network, H2, Hallmark, OWN, Style, etc. just let me know.