I have a Mini, MSE and GM (and yes, I have a problem lol).
MSE has a touch more sub bass while the Mini has a slightly more forward upper bass tuning. I wouldn't necessarily say the Mini's upper bass is higher, but it has slightly scooped upper mids... the timbre is really good but they are a touch pushed back compared to MSE. This lends the perception of higher upper bass but also a bit thicker upper mids. In some ways this means the mini hits a bit harder, but it's at the expense of being a bit less U shaped and certainly less linear/accurate in upper mids and treble. The mini is undeniably relatively more colored in its tuning, but it's quite a pleasant tuning.
Maybe most importantly, the Mini is definitely able to deliver the magic experience of Fatfreq's Bass Cannon technology... you absolutely get the 'wow' bass experience with the Mini too.
The biggest caveat I have is that this epic bass is highly habit forming, indulge at your own risk!