1. Great performances. It's very hard to play sparsely, and even harder to play slowly, and make it compelling. I like what was said "nothing to hide behind". 1000000x agree.
2. Great ambience. Lets be honest. Sparse songs that are super dry can be a little strange in certain genres. Be very careful about recording space and mixing fx. In acoustic recordings picking JUST the right bit of room sound or slight delay or whatever can make it sound much much better.
3. Size. The more dense an arrangement is, the smaller every element can be. This is where a lot of people (myself included) get tripped up because we're so used to carving space it's hard to do LESS of that. It's easy to go in and start gating or putting filters on... The more sparse the more room things have to breathe. So much of this applies in the recording process as well... E.g. Backing mics up a bit to get some depth, using room mics, having fantastic sounding instruments is key.
Try recording guitar in mid-side and recording vocals with a nice full sounding mic. Experiment with mono reverbs or small room stereo reverbs. Experiment with VERY subtle use of a chamber or plate verb. Subtlety is key.