The trouble with Smart TVs is that they can be pretty poorly maintained when it comes to software updates; a year or two in and they're basically abandonware. The only thing I use mine for (app-wise) is Netflix, because all my servers and things are Linux-based and can't do DRM. And the Netflix app is terrible.
If my home setup were Apple centric (and I didn't develop this sort of thing for fun and profit), the Apple TV would be all I'd get.
The reason I recommend it is because you'll be able to access all your content from your various computers -- certainly anything that can be put in iTunes, and that includes movies you rip yourself with third party software like handbrake or source in other ways we won't go into -- and anything that it doesn't provide an app for you can fling at it from one of those devices. And it does have the characteristic Apple virtue that what it does have is less broken than everybody else.
Depending on whether the app's media type and location is supported by Chromecast, the 'source' device may actually be doing the work of fetching and rendering the material and 'casting' the A/V output to Chromecast, but commonly it's just sending the URL and various tokens and chromecast is doing the actual fetching/decoding.
It's similar to having an Airplay-only device on your TV; bearing in mind that they are similar protocols but not the same nor interchangeable. Its main disadvantage is that it can't play content that's local to your network, so if you have your own movies and things you have to play them on your device and screencast it to chromecast. Which may or may not be well supported and look decent. For several good reasons I'd rather tell the TV-attached gizmo "play this file, which you can find over on that computer", than tie up some other device playing it and throwing the video to the TV. You can do the latter with Apple TV as well, but the thing is you don't have to, at least for any content that's supported by iTunes.