I watched enough of the "sprayed limestone" video to know that this method has potential dangers: It's totally reliant on the applicator's artistic ability. I would never get something like this without visiting sites of the applicator's earlier work. (I was not impressed by the ugly "stones" that were being created in the video.) As well, one should review a product's longevity. I couldn't speak to it, but would want to research it before buying.

Personally, I would not want the wall covered in brick next to this house. If it was a direct match, it would be too uninteresting, looking a little like a government project where materials always seems to be bought in unlimited quantities as if the Pentagon was the custtomer. If it was a mismatch, that's not going to be any better. A completely different material -- like stone -- that is compatible, has greater promise. There are so many different stone types and "flagstone" pasted up into the form of a wall is the least attractive. Something that looks like cut blocks that a skilled mason formed would be a much better choice. Look at examples of faux stone and you can find many examples of handsome stone masonry work.

The least expensive decent looking finish is going to be some kind of coating application. (Think special outdoor epoxy-like stuff made for concrete that is in contact with grade.) Stucco will be next. But application varies and it can have a limited life, too. Faux stone will be more expensive but probably the best look and greatest longevity. Real stone would look great, too, but be the most expensive.