I'm not actually sure I agree with the argument that Labour are "just as divided." Certainly there are disagreements within the party, but there is very little ambiguity over who controls the party.
The reason for this isn't necessarily that Labour is better-led, but you always have to remember that Labour's civil war has already been fought and won, largely over the issue of Brexit. The most serious attempt possible to replace Corbyn already took place in its most recent leadership election, and the party's gains in the GE cemented the leadership's position pretty well. Nobody is in any serious position to challenge the leadership.
The Conservatives seem to have at least 3 different power bases within the party: hardline Brexiteers ("led" by JRM and manipulated by Johnson), Disgruntled modernisers/Remainers (rallying behind Hammond but controlled behind the scenes by Heseltine), and the core leadership desperately struggling to mediate (May and the 1922 committee). All except the third are itching for a fight - and the latter are against it because everyone knows they will lose. The Party never properly fought out its leadership contest, so everyone is on the verge of scrambling for it.