I have not heard the Bose product, but do own, have gifted, and have been very impressed with the
Creative SoundBlaster ROAR which is well south of $150, having been replaced by a slightly smaller version the
ROAR 2 (~$150) which I have not listened too.
The original ROAR monitors two BT signals (i.e. tablet for music and mobile phone, allowing music pause to answer a call), has a micro SD slot to play your own music collection. IMHO it is well constructed, travels easily and well (took mine to Kuwait for a month). Recharges through wall wart or USB, when connected to a computer you have additional sound profile modification options, which helped me dial it in a lot.
The original ROAR's bass is very strong, with three options:
normal,
ROAR or Tera Bass selected (more),
ROAR and Tera Bass selected (most). ROAR is akin to a loudness button (emphasize highs and lows) while Tera Bass is a bass only boost, but they can be used together.
I have found just using Tera Bass to be my preference, I primarily listen to jazz, vocals, and classical.
Cheers,
XEagleDriver