[narwan]

Soviet troops have no extra discount on cost. A units cost is simply determined by its statisitics. This cost is modified by the nations experience and morale. Standard cost (as in the encyclopedia) is listed at experience and morale 70.
So if you start a soviet campaign at a period when the country experience/morale is 55/55 your units will be a lot cheaper. Conversely, if you then play the germans who are at that same time at 75/75 their units will be more expensive. Together the cost difference will be enough to give you significant advantage in numbers if playing the soviet side.
The AI is, IMO, less capable with using expensive high quality troops (which require some finesse to handle well) then it is with cheap low quality troops (the 'horde' tactic). But that's not just the AI; using high quality troops well (as they're likely to be outnumbered) is in my experience more difficult for human players too, especially those new to this game.

One trick you can use tomake your battles more difficult is to increase the size of your core force. This will make the AI get a larger force too. Then set-up the troops you bought as 'extras' along your own map edge. On your first turn move them off-map (into the grey). They will be retreated off map and unavailable to you for the rest of the battle. I haven't tried this myself but in theory it should work.

Narwan