The biggest pro is that it runs off a 9V and produces perfect bedroom level sound. Really, if you were in an apartment you might not be able to dime it. It gets plenty of distortion from its own internal gain to get a good hard rocking jam tone. There's a decided lack of bass definition. I expected that, but don't expect tight thrash rhythm tones or anything here.
The other pro is that it's about the same difficultly level as building an od or fuzz pedal, so a perfect beginner level circuit. That's half of why I got it. I teach electronics for audio engineers. I'm thinking about using an LM386 amp for my students as a first soldering project next year.
One additional pro for people is that their website steps through the design of the amp (as well as several classic pedals) step-by-step, so you can understand exactly how it works. Part of my buying the kit was to support their efforts. I bought one of their Arduino daughter-boards to build the digital effects pedal. I'll see how that goes when I get some time this spring.
Overall, I'd recommend one of these for people who've built their own pedals and want a little amp around the house. It sounds perfect fine at bedroom level, and it's an easy build. It's not going to replace my tube amps or anything, and I'd buy a good modeler for quite recording. If I ever get the studio portion of stuff set up at home, I'll record some clips from it.