From what it sounds like, it's a fight who can lead the Klal in the best way based on the same hashkafos. So it's a Machlokes leshem shamayim.
Would seem that if each side compromised and came together in a strong show of achdus, that would be a true solution l'shem shamayim.
Or they could publicize this, cause fights, take it to courts in the US and Israel, avoid BD psaks, and call that machlokes lshem shamayim.
Their choice.
The way you put was disrespectful & offensive.
Depending on which side you are on, the dispute is either to defend or take back what you believe is rightfully yours.
I disparaged the notion that they'd be doing all of this for non-spiritual reasons, and would love to hear of good reasons. I'm trying to be dan litzad zechus.
Sometimes these splits are hashkafa based and I'd prefer that reason more so than a money-based reason.
Besides, when did chasidshe groups become these large money-pots worth fighting over (physically and legally)? Was this already a trend back in Europe, or is it relatively new?