Obviously the most valuable name was Lange and Walter who had fled to the west after the war was in a prime negotiation position being the great grandson of Adolph Lange. I have never read a full accounting of exactly how it went down but without Walter it would be hard to make a new Lange fly and he did not join in with the group that eventually would form the new Glashutte Original, after Lange the next most valuable name. There is reportedly bad blood between Lange and Glashutte over this and there are no ties between them now. Except of course a shared tradition that these new companies would be founded on and is the reason for their similar aesthetic.
I'm bumping this thread because it was recently referenced elsewhere, and wanted to add a little clarification.
Good details above, but the chronology on one crucial thing is off just a bit: Walter Lange and Günter Blümlein re-founded A. Lange & Söhne in 1990, and unveiled their line in 1994, with Glashütte Original being established later in 1994 from the ashes of the old East German conglomerate, VEB Glashütter Uhrenbetriebe (GUB). While it's just a few years, the order of events is a fairly important detail.
The short version is that GUB was created from an amalgam of Glashütte-based watch and "precision mechanics" companies. VEB Mechanik A. Lange & Söhne, Glashütte/Sa., the nationalized post-war Soviet expropriation of ALS by the Soviets, later became Mechanik Lange & Söhne GmbH, before GUB was later founded from the remnants of [A. Lange & Söhne, Uhren-Rohwerke Fabrik Glashütte AG, Otto Estler, Linding & Wolf, R. Mühle, and Gössel & Co. Their early movements that were based on pre-expropriation ALS designs aside-the cal. 28 being notable as being post-occupation but pre-expropriation, Lange's first calibre designed as a wristwatch at Walter's behest-GUB's movements were more or less the horological equivalents of Trabants (until their later days, as the link to Mike's article below illustrates), and by that point the relevant members of the Lange family had been jailed or exiled, with the management of the company left to those more sympathetic to the Soviet cause.
After the Berlin Wall fell, Walter Lange set out in 1989 to relaunch his family company, and a few years later ('94), GUB was privatized, and ostensibly owns the legal rights of the formerly-independent companies amalgamated (though by force) into GUB. I don't know one way or the other, but one would think a deal must have been done for A. Lange & Söhne to regain rights to use their name.
While GO has some superb models that draw from GUB-era designs (e.g., the 20th Century Vintage models), and even from their post-GUB pre-Swatch era (the Quintessentials collection is incredibly strong), despite the larger watchmaking industry F. A. Lange founded (and encouraged the growth of) in Glashütte justifying some of the more traditional features on display (e.g., 3/4 plates, gold chatons, Glashütte stripes, swan neck regulators, etc.), the high overlap of design cues largely stems from Swatch Group's strategic (and astute) decision to purchase and position GO (in 2000) as a more affordable offering against LMH's-and later Richemont's 2000 majority-acquisition of-ALS, an easy wedge given ALS's by then well-established all-precious-metals approach, with the relatively recent Pano series and its mimicry of the 1994 Lange 1 line being a notable example.
If any bad blood does exist between the two (and I don't know anything about that), it's probably that G.O. marketing materials essentially lay claim to the pre-GUB period, which was essentially A. Lange & Söhne's era. Something that, if I was in Walter Lange's shoes in 1994, I don't suppose I'd feel terribly pleased about, either. For example, GO's
history page starts off with a photo of Ferdinand Adolph Lange, Walter's Lange's great-grandfather. They also tread pretty heavily on ALS's designs (of both eras) for their non-20th Century Vintage models, and I include in that the great Quintessentials line, as GO's post-GUB/pre-Swatch-era designs showed their first pre-war aesthetic inclinations (i.e., ALS pocket watches).
Walter Lange's book is worth reading for the history of ALS, and
Mike Stuffler's post provides some excellent movement-specific information and historical background on the GO side.
And as murky (and marketed) as all this is, I'd appreciate any well-sourced corrections to the above. There's a massive amount of confusion out there on the topic, not helped by GO's efforts to anchor their roots in various town-of-Glashütte points of interest. (If you really want to confuse yourself, read up on Strasser & Rohde.)
TL;DR: It's more or less your Shia-Sunni divide in horological form, with the result of the conflict consisting mostly of nice watches.