Cut out generally works very well, which is unsurprising since Adobe's had so long to work on it. The implementation looks and feels more like desktop Photoshop's Quick Selection tool than the scribble in/out method used by Photoshop Touch.
With Smart selection you run your finger over the area you want to keep and it masks out the rest. It does work best with contiguous areas; once you lift your finger it applies the mask and you can't see any other areas to select. Smart selection includes the ability to feather the edges and invert the selection, coupled with the added power of Refine Edges.
When you send the composition to Photoshop, it sends it as the full-resolution image plus a layer mask which you can further refine. There's also more traditional masking option which lets you choose a selection brush size.
But the most interesting aspect of Mix is its initial implementation of a hybrid, almost client-server-like architecture enabled by the SDK. It incorporates the Upright (perspective straightening), shake reduction and content-aware fill features of desktop Photoshop by leveraging cloud computing.
In practice, you choose the tool and the uploads the image to a remote server, which then returns the corrected image to your iPad. It's interesting from a technical perspective, but of mixed practicality.
I should state outright that I have never gotten Shake Reduction to work usefully in Photoshop, and find it even less effective in Mix. Basically, you select it, Mix uploads the image to cloud and sends it back. At that point, it presents you with a variety of samples with different parameters applied, along with an intensity slider so that you can dial back the typically crunchy, artifact-ridden results.
To be fair, shake reduction is difficult. And your mileage may vary. But if you're going to call something a limited-time, premium feature, it had better be worth whatever you're going to charge for it.
Finally, content-aware fill, another feature that I find hit and miss, works fairly well if the photo is just right; there needs to be a lot of similarity in the region surrounding the blighted area or it overblurs or introduces contamination. In Mix, the biggest drawback is waiting for the roundtrip processing from the cloud to find out if you've make a selection mistake. That's not an issue with shake reduction or upright, which affect the entire image.
Performance of all three of the server-based operations is much better on a newer generation iPad; at the very least, Wi-Fi simply transfers faster. I tested Mix on an iPad Air and an iPad 2, and it was only just usable on the latter.
The big picture
As Adobe probably intends, the real advantages of Photoshop Mix are in its links to Creative Cloud and its services. And it does have excellent selection tools and a good interface for overlaying two images -- as long as you don't want to just make one partially transparent, which you can't do.
But there are a few too many frustrations. For instance, you can free rotate a layer, but can't easily rotate it by 90 degrees or flip it. Undo and redo are unreliable. You can't add text.
Ultimately, I'm not quite sure who Mix is for, except perhaps developers who want to see how the hooks into the Creative SDK work, or current CC subscribers who'll use it because the convenience of accessing their CC files makes it worthwhile. If you're just looking for a retouching app that can open from or export to the usual suspects, there's just too much competition.