Personally I see both of these things existing side by side, realistically.
There are two things I think would have a big impact on the social structure of the order: First, the master-apprentice model and the increasing power of magi (and covenants) as they age would, imo, inevitably lead to a lot of patron-client type relationships. Very Roman, which some magi probably quite like. This is not only a likely social order as I see it, it's actually the legal reality in some tribunals like Normandy.
Older magi, or more powerful groups of magi, might "help" a weaker magus/group quite freely - but the expectation is that they follow the lead of the patron and support their positions. "Help" and "collaboration" are more likely to happen when there is a power imbalance, with the more powerful party using their generosity to shape younger magi to their way of thinking.
Second Hermetic society is very splintered. You have houses, mystery cults, lineages, covenants - all with sometimes overlapping, sometimes opposed goals and different views on the sharing of knowledge and resources. For me this means society in the order would inevitably have a strongly cliquey nature. You have in groups and out groups. The in groups cooperate to varying degrees internally, but much less with those outside the group.
However individual magi may be members of more than one group and have complex conflicting loyalties - a Magus might be a member of house Flambeau, but also a member of the neo-Mercurian mystery cult. What happens when another Flambeau is in opposition to the neo-Mercurians? Hard decisions have to be made, and bridges burned. The older magi get the smaller their in-group gets and the more enemies they accumulate (or at least the more friends they lose).
So to answer the initial question the vibe of politics and society varies a lot depending on what group and how high level. To give some (non-comprehensive) examples. These are just based on some groups that have featured in the political side of my most recent saga:
House Bonisagus internally - Very collegiate. A lot of genuine sharing and collaboration. Until someone thinks they are on to a big breakthrough and then suddenly things become a lot more tense. But even then violence between Bonisagi is rare.
House Verditius internally - Complete opposite. Secrecy, pride, and envy are the name of the game. Vendettas are common. Most Verditii are involved in a complex web of enemies and "an enemy of my enemy..." relationships. Everything short of open violence is not only common but approved of. The exception is that within confraternities and certain lineages there is more of a cooperative culture towards initiating members into the mysteries. Stouritus the new Primus has caused the house to split into two factions who might end up in open conflict.
House Jerbiton internally - Very friendly and cooperative. Even more so than Bonisagi. Good relationships with other houses too. The rise of the Antigones is causing a rift within the house however, and they are drifting towards a more aggressive culture.
House Flambeau internally - There is a culture of camaraderie and spirited competition, but Flambeau are one of the houses most willing to engage in actual combat or even wizard's war. There are several sub-cultures within the house who have complex relations with each other. Despite being generally far more friendly with each other it's more common for a Flambeau to kill another Flambeau than for a Verditius to kill a Verditius they have a Vendetta with.
Neo-Mercurian mystery cult - Has members in every house (some more than others) and cooperates closely internally. Mercurian magic and theurgy leads this cult to often have more in common with mercurians from other houses than with magi of their own house. Bitterly opposed to divine influence in the order, and has enemies across many houses because of this.
The Stonehenge Tribunal - Pretty calm in terms of violence. Wizard's Wars are rare. Split into several bitterly opposed political factions with Blackthorn and Voluntas as the two most prominent covenants. A great deal of intrigue and vicious politics (power plays, blackmail, lawsuits, and a lot of slander), but stopping just short of violence.
The Hibernian Tribunal - On the verge of open war between the native Hibernian and the "English" factions. Some magi are literally ignoring the code and killing each other with impunity. The Tremere exarch (Goliard of Blackthorn IMS) is trying to prevent a war breaking out and initiate peaceful legal reforms, but another Tremere faction is undermining her from Coeris and assisting the Tytali in sparking open conflict. Total powder keg.
I think that it's best for these disputes and cut-throat politics to not be 100% the norm order-wide so as to not accidently restrict yourself by invalidating the canon content written about a particular area or group. But within (or between) individual tribunals, or between specific groups, it can work very well.