Lets just get the basics out of the way. The build quality and ease of use is BOSE so it is very good if not great. Simple to use, easy to pair and I really don't know why the provide a user manual. It is that easy to set up.
The Soundlink III is large and heavy for a portable speaker and has a retail price of $300. It sounds great and battery lasts all day. (14 hours according to BOSE however I have never needed to use it that long!)
One thing that the SoundLink Mini has that the regular Soundlink does not is a microphone. I find this nice because you can use the speaker as a speaker phone when paired with your cell phone. Nice for a conference call during meetings and such. (Be darn if I could find the information on Bose site that gives you that information)
The real news is the SoundLink Mini II. The sound is incredible, in fact I might suggest it is better than the full size Soundlink. After reading several reviews I am not the only person that feels that way. A quick tip is to put the unit in a corner and it enhances the bass output. (It can get a bit boomy sometimes depending on the room) I will say that Bose says 10 hours on the battery. At a high volume I would suggest you get 6-7 hours of battery.
The one area that Soundlink II exceeds is outdoors. I am guessing it is due to larger speakers which should produce a larger sound. So if you are mainly using this outdoor at a louder volume I would go with the larger Soundlink II. However let me be clear, the Soundlink II is much heavier, and much larger so you need to evaluate if you are traveling with it. I travel a lot with the Mini and have been very happy. Another item that is handy is the Mini charges with standard mini USB which I already have when traveling where if you travel with the Soundlink II it requires a special Bose connector.
Last is the accessories. The only one I have purchased is the Bose case for the Mini and I do recommend it. It is very protective, light weight, holds the power cord and is not a waste of space.
All in All I recommend the Mini for sound, portability and function. Only caveat is if you are needing longer battery or mainly outdoor use.