Soviets theme was only AI units, Ostheers theme was only AT units, that was changed ages ago. Themes only last until the developers change them because they aren't working.
Sov was all about cheap but large numbers of more mobile units. They couldn't fortify an area very well but were great at attacking quickly and swiftly. This is why their vehicles often can capture territory, because it allows them to retake mass amounts of territory. They had a flexible tech tree so they could surprise their opponent or react quickly. They also had a lot of unit call ins to further diversify their arsenal depending on the scenario.
Ostheer was slower and less mobile, but more powerful when in a fortified position. This is why they had stuff like hull down and better support weapons and could build all sorts of bunkers and mines. They have more rigid teching but much more powerful units. Most of their doctrines were focused on support abilities rather than unit call ins.
Both were also designed for a much faster pace game before the vCoH clowns put a stop to that. VP bleed used to be a tick every 3 seconds (slower than dawn of war 2, faster than CoH1), faster teching and higher lethality. (With coldtech existing to slow the game down a notch.) This is also why Coh1 style sandbags and tanktraps didn't exist and why buildings could be killed quite quickly.
Their themes are mostly intact, although the soviets tech tree was kicked in the balls and ostheer got unit call ins like assault grens and the puma that fuck with the intended game pacing. All the changes to the game itself by the vCoh crowd on the other hand have really taken away from the game. (I enjoyed it most at release, I just come back for the new factions until I get bored.)