I've owned my ATV3 for some years. The picture quality of NowTV via ATV is 'filmic' rather than of broadcast video quality. My broadband download speed is 150Mb.
On vacation, my accommodation had a 2016 Samsung UHD television, which had integral NowTV. The picture quality was of live broadcast quality (not filmic, like ATV). The broadband download speed was just 11Mb.
I think I know the answer, however make sure your ATV is set correct to 50hz so you aren't getting some weird pull down (or up? lol) situation where a 25hz/50hz broadcast is 60hz.
And it could be the NowTV app on the ATV only supports 25hz (filmic looking) whereas the Samsung app had 50hz (live broadcast/soap operas).
However I think the answer really is motion/video interpolation introduced by a Samsung TV you were unfamiliar with. I had my first "run in" with motion interpolation in a similar way.
Samsung calls it "Auto Motion Plus" but all manufacturers have a brand name for it, TruMotion, Natural Motion, etc. Its commonly referred to as the "soap opera effect" (google it).
Normally a TV will display the same frame image a couple to several time because the TVs frame rate is higher than the broadcasts frame rate. However with video interpolation the TV will add transitional frames between the original broadcasts frames. This will give the appearance of a higher frame rate. It will make things known for having filmic frame rates movies look like things known for not having filmic frame rates like live broadcast and soap operas.
The purest in me doesn't like it because its just video processing down after the fact presenting you with something not intended by the content creator. Plus it can introduce digital artifacts. Admittedly in certain things likes sports, news, etc it can look nice.
What brand/model of TV do you have at home? If its an LCD from over the last few years it will likely have a setting for this in the menus.
