I watched some of your video, and the biggest thing I noticed is that you split your corps up into discrete groups composed of all of the same type of units, e.g. all panzers or all infantry. Just like in history, you need a more combined arms approach. A kampfgruppe approach works best in this game. I'd assign at least 6 units to a battle group to maximize damage and minimize losses. Try to soften targets up more with artillery and air before attacking.
http://en.wikipedia.org/wiki/Kampfgruppe
You also need more artillery. A lot more. At least 20% of your core slot, if not more should be artillery. Use wufrahmen or Sturmpanzers, or stick with the towed 10.5 cm or 15 cm, they work wonders against most soft targets.