I would argue that Durkheim seemed to think that the a priori character of space as a unitary frame across all rational beings was a threat to the socially determined plurality of representations of space his empirical approach showed and tried to capture. This, I would argue further, is a misinterpretation since it confused socially determined representation of space(s), which without a doubt can involve plurality in Kant as well, and the pure intuition of space that makes them possible. Thus, there isn't much of a competition between theories since they have different objects they try to explain and the critique isn't valid since it does not criticise the correct level of conditions of the possibility of experience. This kind of critical assessment of Kant, even if Durkheim's motivation is original, is not his own, though: He uncritically uses the arguments of the French neo-kantians Renouvier and, more explicitly, his pupil Hamelin.
My first point was about the motivation for Durkheim. Let me argue with Terry F Godlove Jr. (https://doi.org/10.1002/(SICI)1520-6696(199610)32:4%3C441::AID-JHBS7%3E3.0.CO;2-T):
Durkheim apparently found Kant’s views threatening because he thought they undercut
the possibility of an empirical inquiry into what he saw as the diversity of spatial representation - and so the sort of sociological program that Durkheim wished to inaugurate. [...] Durkheim sees his sociological (empirical) account of spatial representation
as incompatible with Kant’s theory.
Thus, the main premise of Durkheim's critique is the incompatibility with his own, empirical approach to representations of space. Given that, Durkheim looked for arguments against Kant and in his favour.
Once Durkheim had determined that Kant’s views on space were a threat to his project,
he apparently felt he could not proceed absent a compelling reply to them. He found them in
the work of the neo-Kantian Renouvier (1815 - 1903) and in that of his Renouvierist contemporary Hamelin (1856- 1907).
From that, we can conclude that probably, the true aim of the argument of Durkheim is not Kant himself, but a particular French reading of Kant. And that is exactly what Godlove shows us to be the case, after which he concludes:
What is clear is that
Durkheim believed that Hamelin had already answered Kant on technical, purely philosophical grounds, and, in so doing, has shown that our underlying representation of space is not
an a priori intuition but rather a general concept - just the result that Durkheim felt he
I cannot reproduce the whole argument here, but it essentially is about whether the metaphysical exposition of space provided by Kant justifies the priority of a single intuition of boundless space over a general concept of particular spatial structures. Durkheim's sources do deny that, but this does not mean that they are doing justice to Kant:
[I]t appears to me that neither Renouvier nor Hamelin jeopardize Parsons’ recent judgment that Kant’s central phenomenological claims about space
are “on the whole sound.” These claims include the priority of space over objects (we experience objects as in space, and for that reason we cannot construct the concept of space
from relations between objects), and the singularity and boundlessness of space as experienced. If Durkheim is right that these results pose a threat to sociological inquiry into the
form of human spatial representation, his appeal to Hamelin (and, tacitly, to Renouvier) will
be in vain. At the same time, we recognize that this leaves unaddressed the deeper and philosophically most pressing issue, namely, the ground of the phenomenological priority of
space over spaces.
Thus, the philosophical basis of Durkheim's critique is shaky: Even if it may point out some potential problems in the phenomenological parts (3 and 4) of the metaphysical exposition of space, it does so by taking them as stand-alone arguments (part of Godloves greater line of argument) and concludes that the exposition as a whole fails to show what it is supposed to. That is not to say that the critique he builds upon does not have some merit to it. But it is at least questionable that this critique, taken as a stand-alone, justifies the outright rejection and replacement of Kant's transcendental metaphysics and space (singular, boundless) as the a priori form of intuition.
Even worse, Durkheim's original motivation seems to be based on a misunderstanding since there are reasons to assume that pure intuition and general concept are not mutually exclusive:
As I have been urging for the last several paragraphs, Durkheim was deeply right to see Kant’s theory of space as an a priori intuition as
tied to an individualistic conception of epistemology. Whether he correctly perceived its
bankruptcy is another matter. I have tried to sketch - alongside these two critical traditions - a third position which remains genuinely Kantian and which promises peaceful co-existence with Durkheim’s sociological programme. To establish its philosophical cogency
and textual credentials would of course be a much larger undertaking.
That being said, there are good reasons to think that Durkheim's critique is not valid since it only discusses Kant's phenomenological arguments without context and is, therefore, based on an insufficient account of Kant's argument as a whole. Further, Durkheim makes uncritical use of the problematic conclusion that since phenomenologically, space was always relative to objects (probably an unsound premise, see above), the general concept of space as a bounded relation in which objects stand (what Kant will later call relative spaces in his natural philosophy) is actually the most basic kind of space and that Kant's form of intuition is to be discarded. Even worse, guided by a particular early reception of Kant, he sees his probably erroneous premise that his theory was incompatible with Kant's confirmed instead of critically assessing it.
To argue, with Kant, why the pure intuition of space isn't even an object of thought (or representation) and thus the plurality of representations of space does not need to pose a problem to Kant at all (here a summary by Willaschek):
As Kant argues in the “Transcendental Aesthetic,” space
and time are primarily a priori forms of intuition. As Kant acknowledges in a footnote to the B-version of the Transcendental Deduction, however, their status as
forms of intuition as such does not give us representations of space and time as
objects (as they are needed in mathematical thinking) (B 160). The forms of intuition provide us with a manifold of intuition (namely points in space and time),
but as such they do not unite this manifold into intuitive representations of space
and time. This latter kind of representation Kant calls “formal intuition” (B 160),
which results from actively synthesising the manifolds of space and time into
unified representations of space and time as objects (in the widest sense). Hence,
space and time as objects of our representations are not mind-independent
objects, but products of acts of synthesis. (bolder mine)
Thus, Durkheim (with Hamelin) does at the very least confuse the pure forms of intuitions with their (formal) representations.