I've used an ATV3 for a few years just until I got a 4 a couple weeks ago, and they both seem to mirror equally well and fine. For screen mirroring or air playing videos, I've noticed no difference between the 3 and 4.
Keep in mind that there is just a really small amount of lag, and the image on television can compress just briefly if things are moving real fast. If you're wanting to mirror iOS games, I found that the novelty and 'usefulness' of that wore pretty quickly if it's like for a racing game or similar. But it's great for scrolling through text and images and all that.
Also note that iPad will mirror to your HDTV to a 4:3 picture, but a mirrored iPhone will fill the wide screen because they're matching the screen dimensions of the device. I mirrored HitmanGo to my TV recently and it was much more preferable to be mirroring it from my phone rather than from my iPad.
(And none of this applies to "air playing" videos, where it's only sending the video information to your TV and that lag and screen-dimension business is no longer an issue.)
You might have already known most of this, but I hope this helps!
