Question about iPlayer and Netflix on Apple TV

I currently use the Amazon Fire Stick on a good 80 mbps connection, and a Samsung UE32J5100 HD TV. I'm really dissatisfied with how it renders both Netflix and BBC iPlayer: both judder, while the video on Netflix occasionally freezes while the audio continues. Amazon's own content is fine. No amount of changing the settings on the Fire Stick or on the TV seems to alter the problems. So, I've been thinking that maybe I should switch to Apple TV (I know there are independent reasons to do that too, and everything else I own is an Apple product!). But, of course, I don't want to find myself with exactly the same problem on iPlayer and, especially, Netflix. Has anybody else got experience of both, and is able to reassure me that all will be well on Apple TV? Better still, is anybody using Apple TV on the same sort of TV/connection as me and finding things to be OK?