I just fired up a Roku and trying the A&E app for missed shows. Anything I stream through the app is very soft, not sharp HD clarity. If I use the A&E app on my phone to cast to my Chromecast, it starts off fuzzy, but will clear up in a few seconds as the picture buffers. This doesn't happen on the Roku. FWIW, the two sticks are on different parts of my network, but each have a router within 10ft of them, and are on their own SSID, so network speed is not an issue. I stream channels like Foxnews live in clear HD on the Roku just fine, and get about 35-40mbps on the network test.
Is this just how A&E on Roku is? PC and phone are crystal clear as well, the only issue is Roku.