I don't know what is a Brown government. Googling it brings up many results about the former UK Prime Minister's government.
As Soviet Union, the game plays roughly the same without La Resistance as 1.8. The main difference is you need to set up a good garrison template for suppression in your occupied territories. The default one is bad. Soviet Union has the advantage of starting in 1936 with Military Police level 1 already researched, which is useful for garrison templates. You can also set more or less harsh occupation laws, though as Soviet Union you don't really need any extra resources, factories or manpower. I don't quite remember but I think in my last game I kept Civilian Oversight, which is the default, everywhere.
There are several threads in this forum already discussing garrison template compositions, so I won't repeat them. The latest one is:
The suppression values of self-propelled variants have been about cut in half in patch 1.9.3: https://hoi4.paradoxwikis.com/Land_units#Unit_types How do you think does that change optimal garrison templates with and without LaR? I'm still very...
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You can ignore references to Armored Cars, since they're only available in LaR.