DESCRIPTION:
A controlled indoor test with matched volume levels for both speakers, as my early comparison was only a quick improvisation:
http://youtu.be/kgG8xGfPNP4

For medium volume part the Bose Soundlink Mini volume was set to about 60%, the TDK A33 was matched to the same level.

To clarify: the max volume recording at 2:14 does not represent the abolute levels thus is not directly comparable to the medium volume recording before.
You can only compare the relative differences in maximum loudness (and degree of distortion, dynamic compression etc) between both speakers, when played at their maximum volume.