Just got my APP3 delivered and paired up to my ecosystem, right of the bat these fit different to the APP2, and I can use the default medium tips on these rather than the large ones with the APP2.
The sound signature is different as well vs the APP2, seems to be more V shaped with a bit more bass and treble out of the box, it works well on some tracks I guess, but not as great on some. Will need more time to see if I prefer one them snundwise over the APP2s.
The ANC I will have to test a bit later on and I have high hopes that they are noticeably better than the APP2 as that was my main reason to get the APP3.
Yes I have got a case with mine, just a plain simple white silicone one with mine, in fact the same brand as the one I got for my APP2 and it has held up pretty well for the last 2 years or so in constant use.