I have the Bose Soundlink mini, but haven't compared it to the others you mention.
I have compared it to the UE Boom, Kitsound Hive and Bitmore E-Storm.
The Bose is a very nicely made piece of kit, with substantial weight. The sound it puts out is mind boggling for its size. It plays deep bass notes some small hifi speakers couldn't reach. It will play 60hz easily. It plays loud enough too, but the signal processing reins back the bass as you turn up the volume past about 70%.
I could happily live with this as my main source of music if i was on the move a lot or didn't have the space for a home system.
Being critical, the bass could be a little faster, but that's just compared to my home system.
The UE Boom on the other hand struggles to play much lbass below 90hz. It must have a very steep filter to prevent this. My guess is that this is deliberate so the boom can play louder. The Boom can go very loud for a speaker of its size, and has decent punch to the bass, it just sounds wrong when it cuts off entire bass notes from your music collection, where the bose digs deep.
The Boom has usb charging and speaker phone, the bose doesnt.
The Bitmore E-storm is tiny in comparison, but plays very loud for its size and also has decent bass output when positoned correctly. Very nicely made and weighty. Teh bass precision impressed me most with this speaker, it acts like a good sealed box speaker does.
The KS Hive, is like a cheap version of the Bose. It has a big passive radiator and plays a reasonable amount of bass, but not very nice sound or build, but only £50 compared to the Bose's £170. The Bose is well worth the extra though. If you have the space and the cash, the Soundlink III might suit too.