Complex sentence: But the Provisional Government was always somewhat distanced from workers, soldiers, and peasants; the Petrograd Soviet faced no such impediment: they possessed powerful street-level sway of worker and peasant opinions.
Split into simpler sentences: But the Provisional Government was always somewhat distanced from workers, soldiers, and peasants. The Petrograd Soviet, on the other hand, possessed powerful street-level sway of worker and peasant opinions.