I am an old Pz General player who recently discovered Pz Corps (great game!). I won the campaign on Colonel level. I then bought Afrika Corps, and just a couple of days ago, the Grand Campaign dlc. My experience with Bagration discussed below is from the core game's campaign.
The first time you play Bagration is a shocker. The Soviets have hordes of strong armor and good aircraft. I got waxed so bad a couple of times I restarted the entire campaign to put proper emphasis on air power development.
I think I had 6 fighters, including four FW190s (2 were FW190d's), and 3 AA units (including 1 88 FLAK). My strategy was to "hold the line" along the initial setup/river boundary while I eliminated the enemy air power.
Stugs and Pz IVG's are pretty outclassed by the time you get to Bagration, so try to have them upgraded.
I made sure I had 2 King Tigers and 2 Elephant Tds as the backbone of my heavy ground forces. Tigers, Panthers, Pz IVs, stugs, etc. are used to support. Place your artillery where it backs up your infantry. Use your AA to defend your artillery.
The AI will come at you hard. The Elephants can hold the river in the south. Use the KTs to hold the north. Let the AI destroy its army trying to cross the river. You must hold the river line to maintain a defensive advantage, otherwise you'll get overwhelmed!
Once you have gained air superiority, you can more aggressively use your two JU87G's (get these for use in Kursk when they first become available) to hammer the remaining enemy armor. JU88's are good too. The AI will wear its forces down trying to cross the river. Just let them keep coming and hold the line until he's weak enough for you to go on the offensive.
As in Kursk, I found this strategy of letting the enemy attack and get worn down, followed by a counter attack worked.